{"id":2322,"date":"2021-09-29T08:01:29","date_gmt":"2021-09-29T08:01:29","guid":{"rendered":"http:\/\/stgwebsite.mindspark.in\/wordpress\/?page_id=2322"},"modified":"2021-12-31T10:48:02","modified_gmt":"2021-12-31T10:48:02","slug":"trigonometric-ratio-sin-0-value-and-derivation","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/trigonometric-ratio-sin-0-value-and-derivation\/","title":{"rendered":"Trigonometric Ratio: Sin 0\u00b0 – value and derivation"},"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=”4.10.6″ _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
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Trigonometric Ratio: Sin 0\u00b0 – value and derivation<\/b><\/h1>\n

[\/et_pb_text][et_pb_text admin_label=”Text” _builder_version=”4.11.3″ _module_preset=”default” text_font_size=”16px” header_2_font=”|600|||||||” header_2_text_color=”#a01414″ header_3_font=”|600|||||||” custom_padding=”15px|15px||4px|false|false” global_colors_info=”{}”]<\/p>\n

SINE (SIN) 0<\/b>\u00b0<\/b><\/h2>\n

In mathematics, we study trigonometry which deals with the sides and angles of triangles. We can evaluate angles and sides using the various trigonometric ratios. These are the ratios of two sides of a right-angled triangle (90\u00b0 angle). <\/span>Sine, cosine, tangent, cosecant, secant and cotangent – these are the 6 trigonometric ratios.<\/b><\/p>\n

We will learn about the value of Sin 0\u00b0 in this article.<\/span><\/p>\n

A right-angled triangle has two sides and a hypotenuse. The longest side of a right-angled triangle is the hypotenuse.<\/span><\/p>\n

Sin is the ratio of the side opposite to the angle and the hypotenuse of the right-angled triangle.<\/b><\/p>\n

Sin \u019f = side opposite to the angle \u019f\/ hypotenuse<\/span><\/p>\n

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

Let side c be the hypotenuse. The measure of the angle between a and b is 90\u00b0. Since we measure the side opposite the angle \u019f (perpendicular), here<\/span><\/p>\n

Sin \u019f = \\frac {a}{c} <\/span><\/span><\/p>\n

In a right-angled triangle, it is possible to find the values of an unknown side if the value of the other two sides is given. This is done using the Pythagoras theorem. According to this theorem,<\/span><\/p>\n

And here,\u00a0<\/span><\/p>\n

perpendicular^2+base^2=hypotenuse^2 <\/span><\/span><\/p>\n

a<\/span>2<\/sup><\/strong><\/span>+b<\/span>2<\/sup><\/strong><\/span>=c<\/span>2<\/sup><\/strong><\/span><\/p>\n

Now, the other ratios are also combinations of different sides of a triangle. In the table below, you will see how to find the values of all the six trigonometric ratios:<\/span><\/p>\n\n\n\n\n\n\n\n\n\n
Ratios<\/b><\/td>\nFormula<\/b><\/td>\n\u00a0<\/b><\/td>\nReciprocals<\/b><\/td>\n<\/tr>\n
Sin \u019f<\/b><\/td>\nPerpendicular \/ Hypotenuse<\/b><\/td>\na\/c<\/b><\/td>\nCosec \u019f<\/b><\/td>\n<\/tr>\n
Cos \u019f<\/b><\/td>\nBase \/ Hypotenuse<\/b><\/td>\nb\/c<\/b><\/td>\nSec \u019f<\/b><\/td>\n<\/tr>\n
Tan \u019f<\/b><\/td>\nPerpendicular \/ Base<\/b><\/td>\na\/b<\/b><\/td>\nCot \u019f<\/b><\/td>\n<\/tr>\n
Cosec \u019f<\/b><\/td>\nHypotenuse \/ Perpendicular<\/b><\/td>\nc\/a<\/b><\/td>\nSin \u019f<\/b><\/td>\n<\/tr>\n
Sec \u019f<\/b><\/td>\nHypotenuse \/ Base<\/b><\/td>\nc\/b<\/b><\/td>\nCos \u019f<\/b><\/td>\n<\/tr>\n
Cot \u019f<\/b><\/td>\nBase \/ Perpendicular<\/b><\/td>\nb\/a<\/b><\/td>\nTan \u019f<\/b><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u00a0<\/span><\/p>\n

There are standard angles for which the values of the trigonometric ratios are well known. Given below is the trigonometric table for standard angles:<\/span><\/p>\n

 <\/p>\n\n\n\n\n\n\n\n\n\n
\n

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

Ratio<\/b><\/p>\n<\/td>\n

\n

0\u00b0<\/b><\/p>\n

\u00a0<\/b><\/p>\n<\/td>\n

\n

30\u00b0<\/b><\/p>\n

(\u03c0\/6)<\/b><\/p>\n<\/td>\n

\n

45\u00b0<\/b><\/p>\n

(\u03c0\/4)<\/b><\/p>\n<\/td>\n

\n

60\u00b0<\/b><\/p>\n

(\u03c0\/3)<\/b><\/p>\n<\/td>\n

\n

90\u00b0<\/b><\/p>\n

(\u03c0\/2)<\/b><\/p>\n<\/td>\n<\/tr>\n

Sin \u019f<\/b><\/td>\n0<\/span><\/td>\n\u00bd<\/span><\/td>\n1\/\u221a2<\/span><\/td>\n\u221a3\/2<\/span><\/td>\n1<\/span><\/td>\n<\/tr>\n
Cos \u019f<\/b><\/td>\n1<\/span><\/td>\n\u221a3\/2<\/span><\/td>\n1\/\u221a2<\/span><\/td>\n1\/2<\/span><\/td>\n0<\/span><\/td>\n<\/tr>\n
Tan \u019f<\/b><\/td>\n0<\/span><\/td>\n1\/\u221a3<\/span><\/td>\n1<\/span><\/td>\n\u221a3<\/span><\/td>\nNot defined<\/span><\/td>\n<\/tr>\n
Cosec \u019f<\/b><\/td>\nNot defined<\/span><\/td>\n2<\/span><\/td>\n\u221a2<\/span><\/td>\n2\/\u221a3<\/span><\/td>\n1<\/span><\/td>\n<\/tr>\n
Sec \u019f<\/b><\/td>\n1<\/span><\/td>\n2\/\u221a3<\/span><\/td>\n\u221a2<\/span><\/td>\n2<\/span><\/td>\nNot defined<\/span><\/td>\n<\/tr>\n
Cot \u019f<\/b><\/td>\nNot defined<\/span><\/td>\n\u221a3<\/span><\/td>\n1<\/span><\/td>\n1\/\u221a3<\/span><\/td>\n0<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u00a0<\/span><\/p>\n

As we can see, <\/span>the value of sin 0\u00b0 is 0<\/b>.<\/span><\/p>\n

\u00a0<\/span><\/p>\n

DERIVATION OF THE VALUE OF SIN 0\u00b0<\/b><\/h3>\n

Basically, sine is the ratio between the side opposite the angle and the hypotenuse so if we consider sin 0\u00b0 which means that the angle between the hypotenuse and its adjacent side (which is base here) is 0\u00b0. It is only possible when the hypotenuse coincides with the adjacent side thus making the opposite side equal to 0. Thus the ratio becomes 0\/a since RQ (the hypotenuse) coincides with the side PQ.\u00a0<\/span><\/p>\n

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

Therefore, the value of sin 0\u00b0 is 0.<\/span><\/p>\n

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Explore Other Topics<\/h1>\n

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

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Frequently Asked Questions<\/h1>\n
    \n
  1. <\/b> \u00a0 <\/span>What is the value of sin 0\u00b0?<\/b><\/li>\n<\/ol>\n

    Ans:<\/i><\/b> The value of sin 0\u00b0 is 0. It is simply because when the angle is 0, the opposite side does not exist, thus making the ratio 0.<\/span><\/p>\n

    \u00a0<\/span><\/p>\n

      \n
    1. <\/b> \u00a0 <\/span>What is the value of sin 0\u00b0+ cos 0\u00b0+ tan 0\u00b0?<\/b><\/li>\n<\/ol>\n

      Ans:<\/i><\/b> The value of sin 0\u00b0 = 0<\/span>
      \nThe value of cos 0\u00b0 = 1 (from the table)<\/span>
      \nThe value of tan 0\u00b0 = 0 (from the table)<\/span>
      \nTherefore, the value of sin 0\u00b0+ cos 0\u00b0+ tan 0\u00b0 = 0+1+0 = 1<\/span>[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"

      We will derive the value of the trigonometric ratio sin 0\u00b0 which is equal to 0. Also, understand how to find the value of other ratios as well as the value of some standard angles in trigonometry.<\/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":"\nTrigonometric Ratio: Sin 0\u00b0 - value and derivation - mydomain<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/trigonometric-ratio-sin-0-value-and-derivation\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Trigonometric Ratio: Sin 0\u00b0 - value and derivation - mydomain\" \/>\n<meta property=\"og:description\" content=\"We will derive the value of the trigonometric ratio sin 0\u00b0 which is equal to 0. 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