The question is an illustration of trigonometry identity
- The angles are 63 and 117 degrees
- The angles are 13 and 283 degrees
The trigonometry identities are given as:
[tex]\sin(\theta) = 0.891[/tex]
[tex]\cos(\beta) = 0.97437[/tex]
For [tex]\sin(\theta) = 0.891[/tex], take arc sine of both sides
[tex]\theta = \sin^{-1}(0.891)[/tex]
Using a calculator, we have:
[tex]\theta = 63.0^o[/tex]
Because the trigonometry identity is a sine ratio, and the sine of angle is positive in the first and second quadrants.
So, the other angle is in the second quadrant, and it is calculated using:
[tex]\theta = 180 - Angle[/tex]
So, we have:
[tex]\theta = 180^o - 63.0^o[/tex]
[tex]\theta = 117.0^o[/tex]
Hence, the angles are 63 and 117 degrees
For [tex]\cos(\beta) = 0.97437[/tex], take arc cosine of both sides
[tex]\beta = \cos^{-1}(0.97437)[/tex]
Using a calculator, we have:
[tex]\beta = 13.0^o[/tex]
Because the trigonometry identity is a cosine ratio, and the cosine of angle is positive in the first and fourth quadrants.
So, the other angle is in the fourth quadrant, and it is calculated using:
[tex]\beta= 270 + Angle[/tex]
So, we have:
[tex]\beta= 270^o +13.00^o[/tex]
[tex]\beta= 283.00^o[/tex]
Hence, the angles are 13 and 283 degrees
Read more about trigonometry identities at:
https://brainly.com/question/10270672
