Question

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The angle θ lies in Quadrant I .

sinθ = 2/5

What is cosθ ?

Answer 1

Answer:

cosΘ = $\frac{\sqrt{21} }{5}$

Step-by-step explanation:

using the trigonometric identity

• sin²Θ + cos²Θ = 1 , hence

cosΘ = ± $\sqrt{1-sin^2Θ}$

Since Θ is in the first quadrant then cosΘ > 0

cosΘ = $\sqrt{1-(2/5)^2}$

         = $\sqrt{1-4/25}$ = $\sqrt{21/25}$ = $\frac{\sqrt{21} }{5}$

Answer 2

The value of $\cos \theta$ is required.

The value of $\cos\theta=\dfrac{\sqrt{21}}{5}$

$\sin \theta=\dfrac{2}{5}$

We have the identity

$\sin^2\theta+\cos^2\theta=1\\\Rightarrow \cos\theta=\sqrt{1-\sin^2\theta}\\\Rightarrow \cos\theta=\sqrt{1-\left(\dfrac{2}{5}\right)^2}\\\Rightarrow \cos\theta=\sqrt{\dfrac{21}{25}}=\dfrac{\sqrt{21}}{5}$

The value of $\cos\theta=\dfrac{\sqrt{21}}{5}$

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