Question

Henry is asked to find the exact value of cos 10pi/3. His steps are shown below.

Answer 1

Answer:

A) The reference angle should be $\frac{\pi }{3}$, and the sign of the value should be negative.

Step-by-step explanation:

cos($\frac{10\pi }{3}$)

Remove full rotations of 2π until the angle is between 0 and 2$\pi$.

cos($\frac{4\pi }{3}$)

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the third quadrant.

 -cos($\frac{\pi }{3}$)

The exact value of cos($\frac{\pi }{3}$) is $\frac{1}{2}$.

−$\frac{1}{2}$    

Answer 2

Answer:

B.The reference angle should be $\frac{\pi}{3}$ and the cosine value  for $\frac{\pi}{3}$ is $\frac{1}{2}$.

Step-by-step explanation:

We are given that an expression

$cos\frac{10\pi}{3}$

We have to find the exact value of given expression.

Subtract $2\pi$ from $\frac{10\pi}{3}$

$\frac{10\pi}{3}-2\pi=\frac{4\pi}{3}$

Find the reference angle for $\frac{4\pi}{3}$

$\frac{4\pi}{3}-\pi=\frac{\pi}{3}$

$\frac{4\pi}{3}$ lies in III quadrant therefore, $\theta=\theta-\pi$

The value of cosine($\frac{\pi}{3})$

$cos(\frac{\pi}{3})=\frac{1}{2}$

Hence, the reference angle should be $\frac{\pi}{3}$ and the cosine value  for $\frac{\pi}{3}$ is $\frac{1}{2}$.

Option B is true.