{"id":6632,"date":"2021-12-24T07:43:59","date_gmt":"2021-12-24T07:43:59","guid":{"rendered":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/?page_id=6632"},"modified":"2022-01-03T07:30:27","modified_gmt":"2022-01-03T07:30:27","slug":"sin-cos-tan-table-formulas-values-examples-and-faq","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/sin-cos-tan-table-formulas-values-examples-and-faq\/","title":{"rendered":"Sin Cos Tan Table &#8211; Formulas, Values, Examples, and FAQ"},"content":{"rendered":"<p>[et_pb_section fb_built=&#8221;1&#8243; admin_label=&#8221;Section&#8221; module_class=&#8221;mainsec&#8221; _builder_version=&#8221;4.10.4&#8243; _module_preset=&#8221;default&#8221; background_color=&#8221;#e0f2fd&#8221; z_index=&#8221;1&#8243; custom_padding=&#8221;5px||5px||true|false&#8221; locked=&#8221;off&#8221; collapsed=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_row column_structure=&#8221;3_5,2_5&#8243; custom_padding_last_edited=&#8221;on|phone&#8221; _builder_version=&#8221;4.10.8&#8243; _module_preset=&#8221;default&#8221; background_color=&#8221;#FFFFFF&#8221; width=&#8221;100%&#8221; max_width=&#8221;1310px&#8221; custom_padding=&#8221;|51px|40px|51px|false|true&#8221; custom_padding_tablet=&#8221;&#8221; custom_padding_phone=&#8221;|40px|30px|40px|false|true&#8221; border_radii=&#8221;on|10px|10px|10px|10px&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_column type=&#8221;3_5&#8243; admin_label=&#8221;Column L&#8221; _builder_version=&#8221;4.9.10&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_text admin_label=&#8221;Acute Angles<br \/>\n&#8221; _builder_version=&#8221;4.11.3&#8243; _module_preset=&#8221;default&#8221; header_font=&#8221;|700|||||||&#8221; header_text_align=&#8221;left&#8221; header_font_size=&#8221;50px&#8221; header_line_height=&#8221;1.18em&#8221; custom_padding=&#8221;|0px||4px|false|false&#8221; header_font_size_tablet=&#8221;&#8221; header_font_size_phone=&#8221;35px&#8221; header_font_size_last_edited=&#8221;on|phone&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h1>Sin Cos Tan Table &#8211; Formulas, Values, Examples, and FAQ<\/h1>\n<p>[\/et_pb_text][et_pb_text admin_label=&#8221;Text&#8221; _builder_version=&#8221;4.13.1&#8243; _module_preset=&#8221;default&#8221; text_font_size=&#8221;16px&#8221; header_2_font=&#8221;|600|||||||&#8221; header_2_text_color=&#8221;#a01414&#8243; header_3_font=&#8221;|600|||||||&#8221; custom_padding=&#8221;15px|15px|54px|4px|false|false&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h2><b>Sin Cos Tan Table\u00a0<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">The trigonometric functions sin, cos and tan are the primary functions we consider while solving trigonometric questions. \u2018Sin cos tan table\u2019 consists of sin, cos and tan values of standard angles 0\u00b0, 30\u00b0, 45\u00b0, 60\u00b0 and 90\u00b0, sometimes other angles like 180\u00b0, 270\u00b0, and 360\u00b0 also.<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><\/span><\/p>\n<h2><b>Sin Cos Tan Formula<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">The three ratios sin, cos, and tan have their individual formulas. Suppose ABC is a right-angled triangle, right-angled at B, as shown in the figure below:<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"font-weight: 400;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/eistudymaterial.s3.amazonaws.com\/adj-300x201.png\" width=\"401\" height=\"269\" alt=\"\" class=\"wp-image-6635 alignnone size-medium\" srcset=\"https:\/\/eistudymaterial.s3.amazonaws.com\/adj-300x201.png 300w, https:\/\/eistudymaterial.s3.amazonaws.com\/adj.png 422w\" sizes=\"(max-width: 401px) 100vw, 401px\" \/><\/span><\/p>\n<p><span style=\"font-weight: 400;\"><\/span><\/p>\n<p><span style=\"font-weight: 400;\">The three sides in the right-angled triangle are given below:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">AB = Adjacent side to angle \u03b8<\/span><\/p>\n<p><span style=\"font-weight: 400;\">BC = Opposite side to angle \u03b8<\/span><\/p>\n<p><span style=\"font-weight: 400;\">CA = Hypotenuse to angle \u03b8<\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"font-weight: 400;\">Now as per sin, cos and tan formulas, we have:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">sin \u03b8 = Opposite side \/ Hypotenuse = BC \/ CA<\/span><\/p>\n<p><span style=\"font-weight: 400;\">cos \u03b8 = Adjacent side \/ Hypotenuse = AB \/ CA<\/span><\/p>\n<p><span style=\"font-weight: 400;\">tan \u03b8 = Opposite side \/ Adjacent side = CB \/ AB<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><\/span><\/p>\n<h2><b>Sin Cos Tan Chart (Table)<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">Let us see the table where the values of sin, cos, and tan are provided for the standard angles 0\u00b0, 30\u00b0 (\u03c0\/6), 45\u00b0 (\u03c0\/4), 60\u00b0 (\u03c0\/3) and 90\u00b0 (\u03c0\/2).<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"font-weight: 400;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/eistudymaterial.s3.amazonaws.com\/Sin-Cos-Tan-Table-01-300x73.png\" width=\"600\" height=\"146\" alt=\"\" class=\"wp-image-6636 alignnone size-medium\" srcset=\"https:\/\/eistudymaterial.s3.amazonaws.com\/Sin-Cos-Tan-Table-01-300x73.png 300w, https:\/\/eistudymaterial.s3.amazonaws.com\/Sin-Cos-Tan-Table-01-480x117.png 480w, https:\/\/eistudymaterial.s3.amazonaws.com\/Sin-Cos-Tan-Table-01.png 615w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/span><\/p>\n<h2><b><\/b><\/h2>\n<h2><b>How to Remember Sin Cos Tan Values?<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">For finding sin, cos, tan values, follow the below steps:<\/span><span style=\"font-weight: 400;\"><\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Create a table and list the first row with angles 0\u00b0, 30\u00b0, 45\u00b0, 60\u00b0, 90\u00b0, and write the trigonometric function name in the first column, such as sin.<\/span><\/li>\n<\/ul>\n<p style=\"text-align: center;\">\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-02-300x26.png\" width=\"508\" height=\"44\" alt=\"\" class=\"wp-image-6638 alignnone size-medium\" srcset=\"https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-02-300x26.png 300w, https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-02-768x66.png 768w, https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-02-480x41.png 480w, https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-02.png 878w\" sizes=\"(max-width: 508px) 100vw, 508px\" \/><\/p>\n<p style=\"text-align: center;\">\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Now we will determine the values for sin. Write numbers 0, 1, 2, 3, 4 under the angles 0\u00b0, 30\u00b0, 45\u00b0, 60\u00b0, 90\u00b0 respectively.\u00a0<\/span><\/li>\n<\/ul>\n<p style=\"text-align: center;\">\n<p style=\"text-align: center;\"><span style=\"font-weight: 400;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-03-300x26.png\" width=\"508\" height=\"44\" alt=\"\" class=\"wp-image-6639 alignnone size-medium\" srcset=\"https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-03-300x26.png 300w, https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-03-768x66.png 768w, https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-03-480x41.png 480w, https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-03.png 878w\" sizes=\"(max-width: 508px) 100vw, 508px\" \/><\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"font-weight: 400;\"><\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Now divide the numbers by 4 and find the square root. We will get \u221a(0\/4), \u221a(\u00bc), \u221a(2\/4), \u221a(\u00be), and \u221a(4\/4).\u00a0<\/span><\/li>\n<\/ul>\n<p style=\"text-align: center;\">\n<p style=\"text-align: center;\"><span style=\"font-weight: 400;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-04-1-300x26.png\" width=\"508\" height=\"44\" alt=\"\" class=\"wp-image-7256 alignnone size-medium\" srcset=\"https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-04-1-300x26.png 300w, https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-04-1-768x66.png 768w, https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-04-1-480x41.png 480w, https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-04-1.png 878w\" sizes=\"(max-width: 508px) 100vw, 508px\" \/><\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"font-weight: 400;\"><\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">On simplifying this, we will get the values of sine for these 5 angles.\u00a0<\/span><\/li>\n<\/ul>\n<p style=\"text-align: center;\">\n<p style=\"text-align: center;\"><span style=\"font-weight: 400;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-05-1-300x26.png\" width=\"508\" height=\"44\" alt=\"\" class=\"wp-image-7257 alignnone size-medium\" srcset=\"https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-05-1-300x26.png 300w, https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-05-1-768x66.png 768w, https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-05-1-480x41.png 480w, https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-05-1.png 878w\" sizes=\"(max-width: 508px) 100vw, 508px\" \/><\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"font-weight: 400;\"><\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Now for the remaining three angles, use the following formulas:<\/span><span style=\"font-weight: 400;\"><\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">sin (180\u00b0 \u2212 x) = sin x<\/span><\/p>\n<p><span style=\"font-weight: 400;\">sin (180\u00b0 + x) = &#8211; (sin x)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">sin (360\u00b0 \u2212 x) = &#8211; (sin x)<\/span><span style=\"font-weight: 400;\"><\/span><\/p>\n<p><span style=\"font-weight: 400;\">This means,<\/span><\/p>\n<p><span style=\"font-weight: 400;\">sin 180\u00b0 = sin (180\u00b0 \u2212 0\u00b0) = sin 0\u00b0 = 0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">sin 270\u00b0 = sin (180\u00b0 +90\u00b0) = &#8211; (sin 90\u00b0) = -1<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Sin 360\u00b0 = sin (360\u00b0 \u2212 0\u00b0) = &#8211; (sin 0\u00b0) = 0<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"font-weight: 400;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-06-1-300x26.png\" width=\"519\" height=\"45\" alt=\"\" class=\"wp-image-7258 alignnone size-medium\" srcset=\"https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-06-1-300x26.png 300w, https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-06-1-768x66.png 768w, https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-06-1-480x41.png 480w, https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-06-1.png 878w\" sizes=\"(max-width: 519px) 100vw, 519px\" \/><\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"font-weight: 400;\"><\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Now we will determine the values for cos using the formula cos x = sin (90\u00b0 \u2013 x). For example, cos 60\u00b0 = sin (90\u00b0 \u2013 30\u00b0) = sin 30\u00b0 = \u00bd. Similarly, you can find out the other values.<\/span><\/li>\n<\/ul>\n<p style=\"text-align: center;\">\n<p style=\"text-align: center;\"><span style=\"font-weight: 400;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-07-1-300x26.png\" width=\"600\" height=\"52\" alt=\"\" class=\"wp-image-7259 alignnone size-medium\" srcset=\"https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-07-1-300x26.png 300w, https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-07-1-768x66.png 768w, https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-07-1-480x41.png 480w, https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-07-1.png 878w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"font-weight: 400;\"><\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">To determine the values for tan, we use the formula tan x = (sin x\/cos x).<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">For example, the value of tan 30\u00b0 = (sin 30\u00b0\/cos 30\u00b0) = (\u00bd) \/(\u221a3\/2) = (1\/\u221a3). Similarly, we can generate the other values.\u00a0<\/span><\/p>\n<p style=\"text-align: center;\">\n<p style=\"text-align: center;\"><span style=\"font-weight: 400;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-08-1-300x26.png\" width=\"600\" height=\"52\" alt=\"\" class=\"wp-image-7260 alignnone size-medium\" srcset=\"https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-08-1-300x26.png 300w, https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-08-1-768x66.png 768w, https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-08-1-480x41.png 480w, https:\/\/eistudymaterial.s3.amazonaws.com\/Trigonometry-Table-08-1.png 878w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"font-weight: 400;\"><\/span><\/p>\n<p><span style=\"font-weight: 400;\">The value of trigonometric functions for angles ranging from 0\u00ba to 360\u00ba is given in the following trigonometry table.\u00a0<\/span><\/p>\n<p style=\"text-align: center;\">\n<p style=\"text-align: center;\"><span style=\"font-weight: 400;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/eistudymaterial.s3.amazonaws.com\/Sin-Cos-Tan-Table-02-1-300x60.png\" width=\"600\" height=\"120\" alt=\"\" class=\"wp-image-7261 alignnone size-medium\" srcset=\"https:\/\/eistudymaterial.s3.amazonaws.com\/Sin-Cos-Tan-Table-02-1-300x60.png 300w, https:\/\/eistudymaterial.s3.amazonaws.com\/Sin-Cos-Tan-Table-02-1-480x97.png 480w, https:\/\/eistudymaterial.s3.amazonaws.com\/Sin-Cos-Tan-Table-02-1.png 731w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/span><\/p>\n<h2><b><\/b><\/h2>\n<h2><b>Examples<\/b><\/h2>\n<p><b><\/b><\/p>\n<h3><span style=\"font-weight: 400;\">1. What is the value of sin 270\u00b0?<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">We know that, sin 270\u00b0 = sin (180\u00b0 + 90\u00b0)\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Also, sin (180\u00b0 + x) = &#8211; (sin x)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Therefore, sin (180\u00b0 + 90\u00b0) = &#8211; sin 90\u00b0 = &#8211; 1<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Hence, sin 270\u00b0 = &#8211; 1<\/span><\/p>\n<p>&nbsp;<\/p>\n<h3><span style=\"font-weight: 400;\">2. Use the trigonometry table and write the values of:<\/span><\/h3>\n<h3><span style=\"font-weight: 400;\">(a) sin(\u03c0\/4) (b) cos(\u03c0\/3) (c) tan (\u03c0\/2)<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">The trigonometry table helps us to find these values quickly. We have:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">(a) sin(\u03c0\/4) = sin 45\u00ba = (1\/\u221a2)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">(b) cos(\u03c0\/3) = cos 60\u00ba = (1\/2)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">(c) tan (\u03c0\/2) = tan 90\u00ba = \u221e<\/span><\/p>\n<p>[\/et_pb_text][\/et_pb_column][et_pb_column type=&#8221;2_5&#8243; module_id=&#8221;stickysideR&#8221; admin_label=&#8221;Column R&#8221; _builder_version=&#8221;4.10.4&#8243; _module_preset=&#8221;default&#8221; background_color=&#8221;#fdefe0&#8243; custom_padding=&#8221;25px|25px|25px|25px|true|true&#8221; sticky_position=&#8221;top&#8221; sticky_offset_top=&#8221;-280px&#8221; sticky_limit_top=&#8221;row&#8221; sticky_limit_bottom=&#8221;row&#8221; sticky_position_tablet=&#8221;none&#8221; sticky_position_phone=&#8221;none&#8221; sticky_position_last_edited=&#8221;on|desktop&#8221; sticky_limit_bottom_tablet=&#8221;&#8221; sticky_limit_bottom_phone=&#8221;&#8221; sticky_limit_bottom_last_edited=&#8221;on|phone&#8221; 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How to find the value of trigonometric functions sine, cosec and tangent?<br \/><\/strong><\/h3>\n<p><span style=\"font-weight: 400;\"><strong>Ans: <\/strong>All the trigonometric functions relate to the sides of the right-angled triangle, and we can find their values by the following relations:<br \/>Sin = Opposite sides\/Hypotenuse<br \/>Cos = Adjacent sides\/Hypotenuse<br \/>Tan = Opposite sides\/Adjacent sides<strong><br \/><\/strong><\/span><span style=\"font-weight: 400;\"><\/span><\/p>\n<h3><strong>Q2. Why is the value of tan 90\u00b0 not defined in the trigonometry table?<br \/><\/strong><\/h3>\n<p><strong>Ans: <\/strong>The value of tan 90\u00b0 is not defined in a trigonometry table because the value is so large that there is no definite value to assign.<strong><\/strong><\/p>\n<h3><strong>Q3. 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