# If Sin θ = 11 61 , Find the Values of Cosθ Using Trigonometric Identity. - Geometry

#### 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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