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Select all the correct answers. If the measure of angle 0 is 5(pi)/4, which statements are true?
The Measure of the reference angle is 45
cos(0)= √ 2/2
tan(0)=1
sin(0)=√ 2/2
the measure of the referance angle is 30
the measure of the referance angle is 60

Sagot :

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

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