Use Pythagorean identity sint=-4/5, terminal point of t is in quad 4
Since sine is negative and the terminal point of t is in quadrant 4, we can determine that the sine of the reference angle is positive. Therefore, we can write the Pythagorean identity as:
sin^2(t) + cos^2(t) = 1
Using the given information:
sin(t) = -4/5
sin^2(t) = (-4/5)^2 = 16/25
Now we can solve for cos^2(t):
cos^2(t) = 1 - sin^2(t) = 1 - 16/25 = 25/25 - 16/25 = 9/25
Taking the square root of both sides, we get:
cos(t) = ±√(9/25) = ±3/5
Since the terminal point of t is in quadrant 4, cosine is positive in quadrant 4. Therefore, cos(t) = 3/5.
So, the values of sine and cosine for angle t in quadrant 4 are sin(t) = -4/5 and cos(t) = 3/5.