{"id":2794,"date":"2021-10-08T03:46:00","date_gmt":"2021-10-08T03:46:00","guid":{"rendered":"http:\/\/stgwebsite.mindspark.in\/wordpress\/?page_id=2794"},"modified":"2022-01-02T13:45:07","modified_gmt":"2022-01-02T13:45:07","slug":"sin-60-value-and-derivation","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/sin-60-value-and-derivation\/","title":{"rendered":"SIN 60\u00b0 – VALUE AND DERIVATION"},"content":{"rendered":"

[et_pb_section fb_built=”1″ module_class=”mainsec” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#e0f2fd” z_index=”1″ custom_padding=”5px||5px||true|false” locked=”off” global_colors_info=”{}”][et_pb_row column_structure=”3_5,2_5″ custom_padding_last_edited=”on|phone” _builder_version=”4.10.6″ _module_preset=”default” background_color=”#FFFFFF” width=”100%” max_width=”1310px” custom_padding=”|51px|0px|51px|false|true” custom_padding_tablet=”” custom_padding_phone=”|40px|30px|40px|false|true” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}”][et_pb_column type=”3_5″ admin_label=”Column L” _builder_version=”4.9.10″ _module_preset=”default” global_colors_info=”{}”][et_pb_text admin_label=”Acute Angles
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SIN 60\u00b0 – VALUE AND DERIVATION<\/strong><\/h1>\n

[\/et_pb_text][et_pb_text _builder_version=”4.13.1″ _module_preset=”default” text_font_size=”16px” header_2_text_color=”gcid-70a40ab1-38f4-4842-b1ac-1e69b0045607″ header_3_text_color=”#777777″ custom_padding=”|15px||4px|false|false” global_colors_info=”{%22gcid-70a40ab1-38f4-4842-b1ac-1e69b0045607%22:%91%22header_2_text_color%22%93}”]<\/p>\n

The trigonometric ratios measure the ratio of the lengths of the sides of the triangle. We have six such trigonometric ratios namely sin, cosec, cos, sec, tan and cot. We will discuss sin 60\u00b0 in this article. Now, let us take a look at the right-angled triangle.<\/span><\/p>\n

\"\"<\/span><\/p>\n

Here, the longest side c denotes the hypotenuse, a and b denote the other two sides of the right-angled triangle. The side opposite the angle \u019f is the perpendicular which is side a and b is the base.\u00a0<\/span><\/p>\n

\u00a0The following table shows how to calculate the value of the six different ratios:<\/span><\/p>\n

\"\"<\/h2>\n

 <\/p>\n

DERIVATION OF SIN 60\u00b0<\/b><\/h2>\n

Let’s take an equilateral triangle with each angle as 60\u00b0. Now, draw a perpendicular to the line BC. The length of the sides of the triangle is \u2018a\u2019 units. The perpendicular divides the line into half at D, thus making BD = DC = a\/2.<\/span><\/p>\n

\"\"<\/span><\/p>\n

Now, we use Pythagoras theorem to find the length of the perpendicular AD.<\/span><\/p>\n

\u00a0 \u00a0 AD^2+BD^2=AB^2 <\/span>\u00a0<\/span><\/p>\n

\u21d2 AD^2+(a\/2)^2=a^2 <\/span>\u00a0<\/span><\/p>\n

\u21d2 AD^2=a^2-(a\/2)^2 <\/span>\u00a0<\/span><\/p>\n

\u21d2 AD^2=(4a^2-a^2)\/4 <\/span>\u00a0<\/span><\/p>\n

\u21d2 AD^2=3a^2\/4 <\/span>\u00a0<\/span><\/p>\n

\u2234 AD=\\sqrt{3}a\/2 <\/span>\u00a0<\/span><\/p>\n

Now,<\/span><\/p>\n

Sin 60\u00b0 = side opposite the angle\/ hypotenuse<\/span><\/p>\n

Sin 60\u00b0 = (\\sqrt{3}a\/2)\/a<\/span><\/span><\/p>\n

\u21d2 Sin 60\u00b0 = \\sqrt{3}\/2<\/span><\/span><\/p>\n

So, we know from this derivation that sin 60\u00b0 = \\sqrt{3}\/2<\/span>.<\/span><\/p>\n

<\/span><\/p>\n

TRIGONOMETRIC RATIOS AND THEIR VALUES<\/b><\/h2>\n

Trigonometric ratios can be calculated for any angle but there are certain standard angles whose values are shared in the table below.<\/span><\/p>\n

<\/span><\/p>\n

\"\"<\/h2>\n

 <\/p>\n

The table also shows the value of sin 60\u00b0 = \\sqrt{3}\/2<\/span>.<\/span><\/p>\n

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Explore Other Topics<\/h1>\n

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[\/et_pb_text][et_pb_text admin_label=”Related Concepts
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Related Concepts<\/h1>\n

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\n
Sin 30\u00b0<\/a><\/div>\n
Sin 45\u00b0<\/a><\/div>\n
Sin 90\u00b0<\/a><\/a><\/div>\n<\/div>\n

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Frequently Asked Questions<\/h1>\n

1. What is the value of sin 60\u00b0?<\/strong><\/p>\n

Ans:<\/strong> The value of sin 60\u00b0 is \\sqrt{3}\/2<\/span><\/span>.<\/span><\/p>\n

2. What is the value of cosec 60\u00b0?<\/strong><\/p>\n

Ans:<\/strong> Since cosec is the reciprocal of sin so the value of cosec 60\u00b0 is 2\/\\sqrt{3}<\/span><\/span>.<\/span><\/p>\n

3.\u00a0 What is the value of sin 0\u00b0?<\/strong><\/p>\n

Ans:<\/strong> The value of sin 0\u00b0 is 0.<\/span><\/p>\n

[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"

SIN 60\u00b0 – VALUE AND DERIVATIONThe trigonometric ratios measure the ratio of the lengths of the sides of the triangle. We have six such trigonometric ratios namely sin, cosec, cos, sec, tan and cot. We will discuss sin 60\u00b0 in this article. Now, let us take a look at the right-angled triangle. Here, the longest […]<\/p>\n","protected":false},"author":7,"featured_media":0,"parent":714,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"yoast_head":"\nSIN 60\u00b0 - VALUE AND DERIVATION - mydomain<\/title>\n<meta name=\"description\" content=\"Understand about the trigonometric ratio sine 60\u00b0 and its value. 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