# Thread: find the exact value: cos[sin^-1(2/8)]

1. ## find the exact value: cos[sin^-1(2/8)]

thanks

2. Originally Posted by sarabara
thanks
Let $\sin^{-1} \frac{1}{4} = \alpha \Rightarrow \sin \alpha = \frac{1}{4}$.

Now get the value of $\cos \alpha$.

3. Originally Posted by mr fantastic
Let $\sin^{-1} \frac{1}{4} = \alpha \Rightarrow \sin \alpha = \frac{1}{4}$.

Now get the value of $\cos \alpha$.
You can think of this as a right triangle with side opposite $\alpha$ 1 and hypotenuse 4. What is the length of the side near $\alpha$, the third side of this right triangle?

You could also use the fact that $sin^2(\theta)+ cos^2(\theta)= 1$ so that $cos(\theta)= \sqrt{1- sin^2(\theta)}$