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SIN 90\u00b0<\/b><\/h2>\n
Trigonometry is an important branch of mathematics that helps us deal with the sides and angles of a triangle. The trigonometric ratios are the ratios of two sides and Sine is a trigonometric ratio which is simply the ratio of the side opposite to the angle divided by the hypotenuse.\u00a0<\/span><\/p>\n In the above right-angled triangle, the sides are denoted by a, b and c where a is the perpendicular, b is the base and c is the hypotenuse.<\/span><\/p>\n Now, the trigonometric ratio sin is written as the ratio of the side opposite the angle to the hypotenuse and can be written as<\/span><\/p>\n Sin \u019f = Side opposite to the angle \/ Hypotenuse<\/span><\/p>\n Here, the 90\u00b0 angle between sides a and b is opposite the hypotenuse. So when we put the formula, we get<\/span><\/p>\n Sin 90\u00b0 = c \/ c = 1<\/span><\/p>\n There are six trigonometric ratios. They are <\/span>Sine(sin), Cosec(cos), Secant(sec), Tangent(tan) and Cotangent(cot)<\/span>. The table below will show how to find the values of the ratios.\u00a0<\/span><\/p>\n <\/p>\n The common angles for which the values are standardly known are 0\u00b0, 30\u00b0, 45\u00b0, 60\u00b0 and 90\u00b0. The term \u03c0 which is simply interpreted as the 180\u00b0 can be used to write these standard angles. The table below shows the value of the six trigonometric ratios for the standard angles:<\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n As we can see, the table also shows the value of Sin 90\u00b0 = 1.<\/span><\/p>\n \u00a0<\/span><\/p>\n We will use a unit circle to derive the value of sin 90\u00b0.<\/span><\/p>\n Draw a circle with centre O and radius 1 unit.\u00a0<\/span><\/p>\n Now, make a line on the x-axis and then another line that forms the angle \u019f and name that Q. Draw a line perpendicular to the x-axis from Q. In order to derive the value of sin 90\u00b0, we will need to make the angle \u019f as 90\u00b0. We will start by shifting OQ and measuring the angles by shifting anti-clockwise on the circle towards the y-axis. At a point, the OQ line will coincide with the y-axis which will make the value of side opposite \u019f as 1 and the angle as 90\u00b0.<\/span><\/p>\n Thus, giving us the value of sin 90\u00b0 = 1.<\/span><\/p>\n Let us look at an example.<\/span><\/p>\n For example:<\/strong> What is the value of hypotenuse if sin 90\u00b0 is 1 and the length of the opposite side is 7 units?<\/span><\/p>\n Ans:<\/strong> Sin 90\u00b0 = length of the opposite side\/ hypotenuse<\/span><\/p>\n 1 = 7 \/ Hypotenuse<\/span><\/p>\n Therefore, 7 = hypotenuse.\u00a0<\/span><\/p>\n Understand that, the opposite side to sin 90\u00b0 is the hypotenuse only so through these calculations we get the same answer for the hypotenuse.<\/span><\/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 [\/et_pb_text][et_pb_text _builder_version=”4.10.7″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}”]<\/p>\n [\/et_pb_text][et_pb_text admin_label=”Related Concepts [\/et_pb_text][et_pb_text _builder_version=”4.13.1″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}”]<\/p>\n [\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row admin_label=”Row for space” _builder_version=”4.9.11″ _module_preset=”default” locked=”off” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.9.11″ _module_preset=”default” global_colors_info=”{}”][et_pb_divider show_divider=”off” _builder_version=”4.10.4″ _module_preset=”default” global_colors_info=”{}”][\/et_pb_divider][\/et_pb_column][\/et_pb_row][\/et_pb_section][et_pb_section fb_built=”1″ admin_label=”banner and faq Section” module_class=”mainsec2″ _builder_version=”4.10.4″ _module_preset=”default” custom_padding=”40px||0px||false|false” global_colors_info=”{}”][et_pb_row use_custom_gutter=”on” gutter_width=”1″ make_equal=”on” disabled_on=”on|on|off” admin_label=”banner Row” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fff7d6″ width=”100%” max_width=”1310px” height=”134px” custom_margin=”||50px||false|false” custom_padding=”12px||12px||true|false” border_radii=”on|11px|11px|11px|11px” locked=”off” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.9.10″ _module_preset=”default” global_colors_info=”{}”][et_pb_image src=”http:\/\/stgwebsite.mindspark.in\/wordpress\/wp-content\/uploads\/2021\/08\/calloutImage.png” title_text=”calloutImage” show_bottom_space=”off” module_class=”img1″ _builder_version=”4.9.10″ _module_preset=”default” width=”25px” height=”60px” custom_padding=”2px||2px||true|false” global_colors_info=”{}”][\/et_pb_image][et_pb_text module_class=”ftstyle” _builder_version=”4.9.10″ _module_preset=”default” text_orientation=”center” global_colors_info=”{}”]<\/p>\n![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/sin-90.png\")
<\/h2>\n![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/Sin-0-01-300x140.png\")
<\/span><\/p>\n![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/Sin-0-02-300x118.png\")
\u00a0<\/span><\/p>\nDERIVING THE VALUE OF SIN 90\u00b0<\/b><\/h3>\n
![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/sin90_2-300x248.png\")
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\n” _builder_version=”4.9.11″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”25px” text_orientation=”center” custom_margin=”0px||0px||true|false” custom_padding=”8px|15px|0px|15px|false|true” locked=”off” global_colors_info=”{}”]<\/p>\nExplore Other Topics<\/h1>\n
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