Can i please get some help in the follwing math question?

Question

1. An angle with a negative rotation passes through the point (-5, -8). To the nearest degree, what is the measure of the angle?

2. For –180 degrees < A < -90 degrees, which primary trig ratio is positive in this interval? cos A, sin A, or tan A?

3. What is the exact value of sin 5pi/6?

4. What is the exact value of sin –145pi/3?

plz help

Answer 1

1. For the point (-5, -8), -5 represents the adjacent side of a right triangle; -8 represents the opposite side. Use tangent (which equals opposite/adjacent):

tan x = -8/-5

tan x = 1.6

arctan(tan x) = arctan (1.6)

x = 58 degrees

This is the reference angle. To find the angle of rotation, subtract this from 180 degrees:

180-58 = 122 degrees

2. For A to be between -180 and -90 degrees, the angle would be in Quadrant III. The only thing that is positive in quadrant III is tangent (because it is negative/negative, which equals positive...similar to problem #1).

3. 1/2

4. -sqrt(3)/2

Hope that helps!