Maharashtra State Board course SSC (English Medium) Class 10th Board Exam
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If Sin θ = 11 61 , Find the Values of Cosθ Using Trigonometric Identity. - Geometry

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Question

If \[\sin\theta = \frac{11}{61}\], find the values of cosθ using trigonometric identity.

Solution

We have,

\[\sin^2 \theta + \cos^2 \theta = 1\]

\[ \Rightarrow \cos^2 \theta = 1 - \sin^2 \theta\]

\[ \Rightarrow \cos^2 \theta = 1 - \left( \frac{11}{61} \right)^2 \]

\[ \Rightarrow \cos^2 \theta = 1 - \frac{121}{3721} = \frac{3721 - 121}{3721} = \frac{3600}{3721}\]

\[\Rightarrow \cos\theta = \sqrt{\left( \frac{60}{61} \right)^2} = \frac{60}{61}\]

Thus, the value of cosθ is \[\frac{60}{61}\]

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APPEARS IN

 Balbharati Solution for Balbharati Class 10 Mathematics 2 Geometry (2018 to Current)
Chapter 6: Trigonometry
Problem set 6 | Q: 2 | Page no. 138
Solution If Sin θ = 11 61 , Find the Values of Cosθ Using Trigonometric Identity. Concept: Trigonometric Identities.
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