{"id":6274,"date":"2021-12-21T08:24:52","date_gmt":"2021-12-21T08:24:52","guid":{"rendered":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/?page_id=6274"},"modified":"2022-01-03T08:02:40","modified_gmt":"2022-01-03T08:02:40","slug":"sin-table-trigonometry-table-values-examples","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/sin-table-trigonometry-table-values-examples\/","title":{"rendered":"Sin Table – Trigonometry Table – Values – Examples"},"content":{"rendered":"

[et_pb_section fb_built=”1″ admin_label=”Section” 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” collapsed=”off” global_colors_info=”{}”][et_pb_row column_structure=”3_5,2_5″ custom_padding_last_edited=”on|phone” _builder_version=”4.10.8″ _module_preset=”default” background_color=”#FFFFFF” width=”100%” max_width=”1310px” custom_padding=”|51px|40px|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
\n” _builder_version=”4.11.3″ _module_preset=”default” header_font=”|700|||||||” header_text_align=”left” header_font_size=”50px” header_line_height=”1.18em” custom_padding=”|0px||4px|false|false” header_font_size_tablet=”” header_font_size_phone=”35px” header_font_size_last_edited=”on|phone” global_colors_info=”{}”]<\/p>\n

Sin Table – Trigonometry Table – Values – Examples <\/h1>\n

[\/et_pb_text][et_pb_text admin_label=”Text” _builder_version=”4.13.1″ _module_preset=”default” text_font_size=”16px” header_2_font=”|600|||||||” header_2_text_color=”#a01414″ header_3_font=”|600|||||||” custom_padding=”15px|15px|54px|4px|false|false” global_colors_info=”{}”]<\/p>\n

Sin Table<\/b><\/h2>\n

In a right-angled triangle, sine of any acute angle is equal to the ratio of the opposite side to the hypotenuse.<\/span><\/p>\n

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

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

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

\\operatorname{Sin} \\theta=\\frac{\\text { Side opposite to } \\theta}{\\text { Hypotenuse }}<\/span><\/span><\/p>\n

Angles are measured in degrees or radians. To convert degrees into radians, multiply \\left(\\frac{\\pi}{180^{\\circ}}\\right)<\/span><\/span>with the given degree.<\/span><\/p>\n

There are some standard angles that are frequently used for calculations and the sin values of these angles should be remembered. These standard angles are 0\u00b0, 30\u00b0, 45\u00b0, 60\u00b0 and 90\u00b0.<\/span><\/p>\n

Sin table is the part of the trigonometry table. It shows the values for sine of standard angles.\u00a0<\/span><\/p>\n

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

Sin Table for standard angles<\/b><\/h2>\n

<\/b><\/p>\n

\"\"<\/b><\/p>\n

<\/b><\/p>\n

Trick to remember the above table<\/b><\/p>\n

1. Write the standard angles in ascending order.<\/span><\/p>\n

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

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

2. Under these angles write 0 to 4 from left to right and divide them by 4.<\/span><\/p>\n

\n

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

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

3. Take the square roots of the numbers shown in step 2.<\/span><\/p>\n

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

\"\"<\/p>\n

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

4. Compile the table in step 1 and step 3.<\/span><\/p>\n

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

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

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

Formulas used in calculations<\/b><\/h2>\n

Given below are some basic formulas used in solving problems related to trigonometry.<\/span><\/p>\n

Complementary angles formula<\/b><\/p>\n

1. \\sin x=\\cos \\left(90^{\\circ}-x\\right)<\/span>
2. \\cos x=\\sin \\left(90^{\\circ}-x\\right)<\/span>
3. \\tan x=\\cot \\left(90^{\\circ}-x\\right)<\/span>
4. \\cot x=\\tan \\left(90^{\\circ}-x\\right)<\/span>
5. \\sec x=\\operatorname{cosec}\\left(90^{\\circ}-x\\right)<\/span>
6. \\operatorname{cosec} x=\\sec \\left(90^{\\circ}-x\\right)<\/span><\/b><\/p>\n

<\/b><\/p>\n

Reciprocal Formulas<\/b><\/p>\n

\\text { 1. } 1 \/ \\sin x=\\operatorname{cosec} x<\/span><\/b><\/p>\n

2.\u00a0 1\/ \\cos x=\\sec x<\/span>
3.\u00a0 1\/ \\tan x=\\cot x<\/span><\/b><\/p>\n

<\/b><\/p>\n

We have also given the sine values from 0 degrees to 90 degrees for your reference.<\/span><\/p>\n

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

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

Sin chart (0\u00b0 to 90\u00b0)<\/b><\/h2>\n

\"\" \"\" \"\"<\/b><\/p>\n

<\/b><\/p>\n

<\/b><\/h2>\n

Solved Examples <\/b><\/h2>\n

1. What is the value of cos 45\u00b0?<\/b><\/h2>\n

cos 45\u00b0 = sin (90\u00b0 – 45\u00b0)\u00a0<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 = sin 45\u00b0<\/span><\/p>\n

= \\frac{1}{\\sqrt{2}}<\/span><\/p>\n

 <\/p>\n

2.<\/strong> Find the value of cot 30\u00b0.<\/b><\/p>\n

Sin 30\u00b0 = \u00bd<\/span><\/p>\n

Cos 30\u00b0 = sin (90\u00b0 – 30\u00b0)\u00a0<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= sin 60\u00b0\u00a0<\/span><\/p>\n

= \\frac{\\sqrt{3}}{2}<\/span><\/p>\n

\\cot 30^{\\circ}=\\frac{\\cos 30^{\\circ}}{\\sin 30^{\\circ}}=\\frac{\\sqrt{3} \/ 2}{1 \/ 2}=\\sqrt{3}<\/span><\/b><\/p>\n

<\/b><\/p>\n

Hence the value of cot 30\u00b0 is equal to\\sqrt{3}<\/span><\/span><\/b><\/p>\n

3. Calculate the value of (cos 45\u00b0 – sin 30\u00b0).<\/b><\/p>\n

<\/b><\/p>\n

\\cos 45^{\\circ}=\\frac{1}{\\sqrt{2}}<\/span>
\\sin 30^{\\circ}=\\frac{1}{2}<\/span>
\\cos 45^{\\circ}-\\sin 30^{\\circ}=\\frac{1}{\\sqrt{2}}-\\frac{1}{2}=\\frac{\\sqrt{2}-1}{2}<\/span>
Hence the value of \\left(\\cos 45^{\\circ}-\\sin 30^{\\circ}\\right)<\/span> is equal to \\frac{\\sqrt{2}-1}{2}<\/span><\/b><\/p>\n

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

<\/b><\/p>\n

<\/b><\/p>\n

[\/et_pb_text][\/et_pb_column][et_pb_column type=”2_5″ module_id=”stickysideR” admin_label=”Column R” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fdefe0″ custom_padding=”25px|25px|25px|25px|true|true” sticky_position=”top” sticky_offset_top=”-280px” sticky_limit_top=”row” sticky_limit_bottom=”row” sticky_position_tablet=”none” sticky_position_phone=”none” sticky_position_last_edited=”on|desktop” sticky_limit_bottom_tablet=”” sticky_limit_bottom_phone=”” sticky_limit_bottom_last_edited=”on|phone” border_radii=”on|15px|15px|15px|15px” box_shadow_style=”preset3″ global_colors_info=”{}”][et_pb_image src=”https:\/\/eistudymaterial.s3.amazonaws.com\/1080×1080.png” alt=”Free Trial banner” title_text=”Mindspark Free Trial Banner” url=”https:\/\/mindspark.in\/free-trial” align=”center” module_class=”adsimg” _builder_version=”4.11.1″ _module_preset=”default” custom_padding=”||||false|false” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}” transform_styles__hover_enabled=”on|hover” transform_scale__hover_enabled=”on|hover” transform_translate__hover_enabled=”on|desktop” transform_rotate__hover_enabled=”on|desktop” transform_skew__hover_enabled=”on|desktop” transform_origin__hover_enabled=”on|desktop” transform_scale__hover=”102%|102%”][\/et_pb_image][et_pb_text admin_label=”Explore Other Topics
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Explore Other Topics<\/h1>\n

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\n
Geometry<\/a><\/div>\n
Trigonometry<\/a><\/div>\n
Operations<\/a><\/div>\n
Numbers<\/a><\/div>\n<\/div>\n

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

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\n
Table of Trigonometry<\/a><\/div>\n
Sin Cos Tan Table<\/a><\/div>\n
Trigonometry all Formulas<\/a><\/a><\/div>\n<\/div>\n

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Start Free Trial<\/a><\/p>\n<\/div>\n<\/div>\n<\/div>\n

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<\/h1>\n

Frequently Asked Questions\u00a0<\/span><\/span><\/h1>\n
    <\/ol>\n

    Q1. What is a sin table?
    <\/strong><\/h3>\n

    Ans: <\/strong><\/span>Sin table is the part of the trigonometry table. It shows the values for sine of standard angles 0\u00b0, 30\u00b0, 45\u00b0, 60\u00b0 and 90\u00b0.<\/span><\/strong><\/strong><\/span><\/span><\/strong><\/p>\n

    Q2. Define sine ratio?<\/strong><\/h3>\n

    Ans: <\/strong>In a right-angled triangle, the sine ratio of any acute angle is equal to the ratio of the opposite side to the hypotenuse.
    \\operatorname{Sin} \\theta=\\frac{\\text { Side opposite to } \\theta}{\\text { Hypotenuse }}<\/span><\/strong><\/p>\n

    Q3. Define Cos ratio?<\/strong><\/h3>\n

    Ans:\u00a0 <\/strong>In a right-angled triangle, the cos ratio of any acute angle is equal to the ratio of the adjacent side to the hypotenuse.<\/span><\/p>\n

    \\operatorname{Cos} \\theta=\\frac{\\text { Side adjacent to } \\theta}{\\text { Hypotenuse }}<\/span><\/span><\/p>\n

    Q4. Define tan ratio?<\/b><\/strong><\/h3>\n

    Ans:\u00a0 <\/strong>In a right-angled triangle, the tan ratio of any acute angle is equal to the ratio of the opposite side to the adjacent side<\/span><\/p>\n

    \\operatorname{Tan} \\theta=\\frac{\\text { Side opposite to } \\theta}{\\text { Side adjacent to }\\theta}<\/span>\u00a0<\/span><\/p>\n

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

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

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