Question

if 0= 2pi/3, then the value of cos 0= -1/2.Part A: What is another angle, 0, that has the same value of cos 2pi/3, if 0<0<2pi?Part B: Name two angles that have the opposite value of cos 2pi/3, if 0<0<2pi.

Answer 1

The other angle with the same value of 2pi/3 for the cosine function is given by:

$\frac{2\pi{}}{3}+\frac{\pi{}}{2}=\frac{7\pi{}}{6}$

Because the cosine and sine function repeat the absolute value every pi/2, to localize the sign you can think about the trigonometric circle.

As I stated before the cosine and sine function repeat the absolute value every pi/2, to localize the sign you can think about the trigonometric circle. The values between pi/2 and 3pi/2 are negative and the others are positive.

B part)

To find the two values with the opposite value we need to take pi/2 from our angle, and add pi to find the two values.

$\frac{2\pi}{3}+\pi=\frac{5\pi}{3}$

and

$\frac{2\pi}{3}-\frac{\pi}{2}=\frac{\pi}{6}$

With this we have all the angles.