Question

if sin theta is equals to 11 upon 61 find the value of cos theta using trigonometry identity

Answer 1

${ \sin}^{2} \theta + {cos}^{2} \theta = 1 \\ = > \cos( \theta) = \sqrt{1 - {sin}^{2}\theta } \\ = \sqrt{1 - { (\frac{11}{61}) }^{2} } \\ = \sqrt{ \frac{3600}{3721} } \\ = \frac{60}{61}$
hope it helps

Answer 2

We know :

sinθ = Opposite Side/Hypotenuse

To Find :

Value of cosθ

Solution :

cosθ = Adjacent Side/Hypotenuse

cosθ = Adjacent Side/61

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• Using Pythagoras Theorem

(Hypotenuse)² = (Opposite side)² + (Adjacent Side)²

⇒ (61)² = (11)² + (Adjacent Side)²

⇒ 3721 = 121 + (Adjacent Side)²

⇒ 3721 - 121 = (Adjacent Side)²

⇒ 3600 = (Adjacent Side)²

⇒ 60 = Adjacent Side

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cosθ = 60/61