Write trig function in terms of another. Tan(t) sin(t) in quadrant 4
Since we are in quadrant 4, both the sine and tangent functions will be positive.
In quadrant 4, we know that the sine function is positive and the cosine function is negative. Therefore, we can write sin(t) = sqrt(1 - cos^2(t)).
Using the Pythagorean trigonometric identity, we know that sin^2(t) + cos^2(t) = 1. Solving for cos^2(t), we get cos^2(t) = 1 - sin^2(t). Therefore, cos(t) = -sqrt(1 - sin^2(t)).
Now, we can write tan(t) = sin(t)/cos(t) = sqrt(1 - sin^2(t)) / -sqrt(1 - sin^2(t)) = -1.
Hence, tan(t) = -1.