Question

Select all the correct answers. If the measure of angle 0 is 5(pi)/4, which statements are true?

Answer 1

Finding the equivalent angle of $\theta$, the correct statements are given as follows:

• The Measure of the reference angle is 45.

• $\cos{\theta} = \frac{\sqrt{2}{2}}$.

• $\tan{\theta} = 1$

• $\sin{\theta} = \frac{\sqrt{2}{2}}$.

What are equivalent angles?

Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.

In this problem, the given angle is as follows:

$\theta = \frac{5\pi}{4}$

It is on the third quadrant, as it is between pi and 1.5 pi, hence the equivalent on the first quadrant, also known as the reference angle, is given by:

$\frac{5\pi}{4} - \pi = \frac{5\pi}{4} - \frac{4\pi}{4} = \frac{\pi}{4}$

The angle of 45º has equal sine and cosine, and tangent of 1, hence the correct statements are:

• The Measure of the reference angle is 45.

• $\cos{\theta} = \frac{\sqrt{2}{2}}$.

• $\tan{\theta} = 1$

• $\sin{\theta} = \frac{\sqrt{2}{2}}$.

More can be learned about equivalent angles at brainly.com/question/24787111

#SPJ1