SOLUTION: One solution to the equation (-4/5) = sin(x) is approx -53.130 What is the NEXT real solution to the right? A) x=180 + |-53.130| B) x=-233.13 C) x=-53.130 + 180 D) x=360 + (-5

Click here to see ALL problems on Trigonometry-basics

Question 1151678: One solution to the equation (-4/5) = sin(x) is approx -53.130
What is the NEXT real solution to the right?
A) x=180 + |-53.130|
B) x=-233.13
C) x=-53.130 + 180
D) x=360 + (-53.130)
E) none of these
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
sine is negative in the third and fourth quadrant.
if sin(x) = -4/5, then x = -53.13010235 degrees.
that's in the fourth quadrant.
the equivalent angle in the first quadrant would be 360 - 306.8698976 = 53.13010235 degrees.
the equivalent angle in the third quadrant would be 180 + 53.13010235 = 233.13010235 degrees.
that would be 180 + absolute value of (-53.130) degrees.
to see if is the next solution to the right, graph the equation of y = sin(x).
here's what it looks like.
-53 is in the fourth quadrant.
going to the right, the next angle with sine of -4/5 is in the third quadrant of the next full 360 degree cycle.

you can see that the next angle to the right of -53.13... that has a sine of -4/5 is 233.13... degrees.

i always get the equivalent angle in the first quadrant.
that's called the reference angle.
from the first quadrant, it's easiest to go to any other quadrant you want.
second quadrant angle is 180 minus the reference angle.
third quadrant angle is 180 plus the reference angle.
fourth quadrant angle is 360 minus the reference angle.
those would all be positive angles.
equivalent negative angles would be those angles minus 360 degrees.