Question

If $\displaystyle{\sf\:17\:\sin\:\theta\:=\:8}$

Then Find cos theta =? ​

Answer 1

❍Given :-

• $\displaystyle{\sf\:17\:\sin\:\theta\:=\:8}$

We have to find the value of $\sf cos\:\theta$

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$\displaystyle{\sf\:17\:\sin\:\theta\:=\:8}$

$:\displaystyle{\implies\sf\:\sin\:\theta\:=\:\dfrac{8}{17}}$

❍ We know that:-

$\displaystyle{\red{\sf\:\sin^2\:\theta\:+\:\cos^2\:\theta\:=\:1}\sf\:\:\:-\:-\:-\:[\:Trigonometric\:identity\:]}$

$\displaystyle{\implies\sf\:\cos^2\:\theta\:=\:1\:-\:\sin^2\:\theta}$

$\displaystyle{\implies\sf\:\cos\:\theta\:=\:\sqrt{1\:-\:\sin^2\:\theta}\:\:\:-\:-\:-\:[\:Taking\:square\:roots\:]}$

$\displaystyle{\implies\sf\:\cos\:\theta\:=\:\sqrt{1\:-\:\left(\:\dfrac{8}{17}\:\right)^2}}$

$\displaystyle{\implies\sf\:\cos\:\theta\:=\:\sqrt{1\:-\:\dfrac{8^2}{(\:17\:)^2}}\:\:\:\:-\:-\:-\:\left[\:\because\:\left(\:\dfrac{a}{b}\:\right)^m\:=\:\dfrac{a^m}{b^m}\:\right]}$

$\displaystyle{\implies\sf\:\cos\:\theta\:=\:\sqrt{1\:-\:\dfrac{64}{289}}}$

$\displaystyle{\implies\sf\:\cos\:\theta\:=\:\sqrt{\dfrac{289\:-\:64}{289}}}$

$\displaystyle{\implies\sf\:\cos\:\theta\:=\:\sqrt{\dfrac{225}{289}}}$

$\displaystyle{\implies\sf\:\cos\:\theta\:=\:\sqrt{\dfrac{15\:\times\:15}{17\:\times\:17}}}$

$\displaystyle{\implies\boxed{\red{\sf\:\cos\:\theta\:=\:\dfrac{15}{17}}}}$

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