Use the figure to find the exact value of the trigonometric function.
Cos 2β

A)
B)
D)

Question

Use the figure to find the exact value of the trigonometric function. ​   ​
Cos 2β
​
A)​ 
B)​ 
D)​

Quizplus · Accepted Answer

We can use the double angle formula for cosine: 
$$\cos 2\beta = 2\cos^2 \beta - 1$$ 
From the figure, we see that the adjacent side to $\beta$ is 1, and the hypotenuse is $\sqrt{2}$. Therefore, $\cos \beta = \frac{1}{\sqrt{2}}$. 
Substituting into the double angle formula: 
$$\cos 2\beta = 2\left(\frac{1}{\sqrt{2}}\right)^2 - 1 = 1 - 1 = 0$$ 
Therefore, the answer is C.

Use the Figure to Find the Exact Value of the Trigonometric