Finding the equivalent angle of [tex]\theta[/tex], the correct statements are given as follows:
- The Measure of the reference angle is 45.
- [tex]\cos{\theta} = \frac{\sqrt{2}{2}}[/tex].
- [tex]\tan{\theta} = 1[/tex]
- [tex]\sin{\theta} = \frac{\sqrt{2}{2}}[/tex].
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:
[tex]\theta = \frac{5\pi}{4}[/tex]
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:
[tex]\frac{5\pi}{4} - \pi = \frac{5\pi}{4} - \frac{4\pi}{4} = \frac{\pi}{4}[/tex]
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.
- [tex]\cos{\theta} = \frac{\sqrt{2}{2}}[/tex].
- [tex]\tan{\theta} = 1[/tex]
- [tex]\sin{\theta} = \frac{\sqrt{2}{2}}[/tex].
More can be learned about equivalent angles at https://brainly.com/question/24787111
#SPJ1
