Question

If `sin theta=(7)/(25)`​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

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Proper Question :-

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$\sf\bold{\red{if \: sin∅ \: = \frac{7}{25 \: } \: \: then \: \: find \: \: cos∅ \: \: and \: \: tan∅ }}$

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Used Formula :-

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$\sf\bold{\purple{ sin∅ \: = \: \frac{oppsite \: side}{hypotenuse} }}$

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$\sf\bold{\green{ cos∅ \: = \: \frac{adjecent\: side}{hypotenuse} }}$

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$\sf\bold{\blue{ tan∅ \: = \: \frac{oppsite \: side}{adjecent \: side} }}$

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Answer :-

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In ∆ABC , By Pythagoras Therom .

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$\implies \bf \: AB² + BC² = AC²$

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$\implies \bf \: (7k)² + BC² = (25K)²$

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$\bf \implies \: 49K² + BC ² = 625K²$

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$\bf \implies \: BC² = 625K² - 49K²$

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$\implies \bf \: BC² = 576K²$

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$\bf \implies \: BC = 24K$

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Now We Get Answer...

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$\sf\bold{{ cos∅ \: = \: \frac{adjecent\: side}{hypotenuse} }}$

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$\bf \: cos∅ \: = \: \frac{BC}{AC} \bf \: = \frac{24K}{25K} = \frac{24}{25}$

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$\bf \: cos∅ \: = \frac{24}{25}$

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Now ,

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$\sf\bold{{ tan∅ \: = \: \frac{oppsite \: side}{adjecent \: side} }}$

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$\bf \: tan∅ \: = \frac{AB}{BC} = \frac{7K}{24K} = \frac{7}{24}$

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$\bf \: tan∅ \: = \frac{7}{24}$

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Learn More :-

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$\begin{gathered}\sf \color{aqua}{Trigonometry\: Table}\\ \blue{\boxed{\boxed{\begin{array}{ |c |c|c|c|c|c|} \sf \red{\angle A} & \red{\sf{0}^{ \circ} }&\red{ \sf{30}^{ \circ} }& \red{\sf{45}^{ \circ} }& \red{\sf{60}^{ \circ}} &\red{ \sf{90}^{ \circ}} \\ \hline \\ \rm \red{sin A} & \green{0} & \green{\dfrac{1}{2}}& \green{\dfrac{1}{ \sqrt{2} }} &\green{ \dfrac{ \sqrt{3}}{2} }&\green{1} \\ \hline \\ \rm \red{cos \: A} & \green{1} &\green{ \dfrac{ \sqrt{3} }{2}}&\green{ \dfrac{1}{ \sqrt{2} }} & \green{\dfrac{1}{2}} &\green{0} \\ \hline \\\rm \red{tan A}& \green{0} &\green{ \dfrac{1}{ \sqrt{3} }}&\green{1} & \green{\sqrt{3}} & \rm \green{\infty} \\ \hline \\ \rm \red{cosec A }& \rm \green{\infty} & \green{2}& \green{\sqrt{2} }&\green{ \dfrac{2}{ \sqrt{3} }}&\green{1} \\ \hline\\ \rm \red{sec A} & \green{1 }&\green{ \dfrac{2}{ \sqrt{3} }}& \green{\sqrt{2}} & \green{2} & \rm \green{\infty} \\ \hline \\ \rm \red{cot A }& \rm \green{\infty} & \green{\sqrt{3}}& \green{1} & \green{\dfrac{1}{ \sqrt{3} }} & \green{0}\end{array}}}}\end{gathered}$

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More Info :-

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Trigonometry, as the name might suggest, is all about triangles.

More specifically, trigonometry is about right-angled triangles, where one of the internal angles is 90°. Trigonometry is a system that helps us to work out missing or unknown side lengths or angles in a triangle..

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Trigonometry is a branch of applied mathematics concerned with the relationship between angles and their sides and the calculations based on them. First developed as a branch of geometry focusing on triangles during the third century BC, trigonometry was used extensively for astronomical measurements. The major trigonometric functions, including sine, cosine, and tangent, were first defined as ratios of sides in a right triangle. Since trigonometric functions are intrinsically related, they can be used to determine the dimensions of any triangle given limited information. In the eighteenth century, the definitions of trigonometric functions were broadened by being defined as points on a unit circle. This definition for the development of graphs of functions related to the angles they represent, which were periodic. Today, using the periodic nature of trigonometric functions, mathematicians and scientists have developed mathematical models to predict many natural periodic phenomena.

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