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# If Sin θ = 7 25 , Find the Values of Cosθ and Tan​θ - Geometry

ConceptApplication of Trigonometry

#### Question

If $\sin\theta = \frac{7}{25}$, find the values of cosθ and tan​θ.

#### Solution

We have,
$\sin^2 \theta + \cos^2 \theta = 1$
$\Rightarrow \left( \frac{7}{25} \right)^2 + \cos^2 \theta = 1$
$\Rightarrow \cos^2 \theta = 1 - \frac{49}{625} = \frac{625 - 49}{625} = \frac{576}{625}$

$\Rightarrow \cos\theta = \sqrt{\frac{576}{625}} = \frac{24}{25}$
Now,
$\tan\theta = \frac{\sin\theta}{\cos\theta}$
$\Rightarrow \tan\theta = \frac{\frac{7}{25}}{\frac{24}{25}}$
$\Rightarrow \tan\theta = \frac{7}{24}$
Thus, the values of cosθ and tanθ are $\frac{24}{25}$ and $\frac{7}{24}$, respectively.

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#### APPEARS IN

Solution If Sin θ = 7 25 , Find the Values of Cosθ and Tan​θ Concept: Application of Trigonometry.
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