trig problem can you help??

Question

find the exact value under the given conditions:

cos alpha = (sq root 5) / 5 . . . . 0
sin beta = -4/5 . . . . . -pi/2

please help and explain thanks

Answer 1

Alpha (let's call it A) is in quadrant one. Cos A = sqrt 5/5
so x = sqrt 5 and r = 5. Using the Pythagorean theorem

x^2 + y^2 = r^2, so y = sqrt 20 = 2 sqrt 5.
What are you supposed to find?
The other angle values are
sin A = y/r = ( 2 sqrt 5)/5, tan A = y/x = 2
And the others are just reciprocals.

Problem 2: Beta (B) is in the 4th quadrant. y = -4, r = 5, so x = 3. (x is positive in quadrant 4)

cos B = x/r = 3/5
tan B = y/x = -4/3
Etc.