Question

If the given point is on the terminal arm of an angle A in standard position, angle A is greater than or equal to 0 degrees and it is less than or equal to 180 degrees, find the measure of angle A, to the nearest tenth of a degree.
a) (4,3)
b) (12,5)
c) (-6,8)
d) (-24,7)

PLEASE help me!! with the steps and all i have no idea about this... thankyou so much!!

Answer 1

If you are just learning this, I suggest you make a sketch of the right-angled triangle
a) and b) will be in quadrant I
c) and d) will be in quadrant II

I will do b) and c)

b) by Pythagoras, it is easy to find the hypotenuse to be 13
since cosØ = 12/13
use the cosine inverse of your calculator...
enter:
2nd
cos
(12÷13)
= to get appr 22.62° or 23°

c) hypotenuse^2 = (-6)^2 + 8^2 = 100
hypot = √100 = 10
cosØ = -6/10 = -3/5 or -.6

enter:
2nd
cos
(-.6)
=
to get 126.87° or 127°