Explanation:
I believe there is something missing from the description.
I base my solution and explanation on the following assumptions :
- the angle theta is at the origin (0, 0).
- not only passes the terminal side through (20, -21), but so does also the circle around our trigonometric triangle.
in other words, (20, -21) is not just any point on the line, but it is the upper vertex of the triangle.
the baseline of the triangle, which is the radius of the surrounding circle is then the distance from the origin to the point.
Pythagoras (= distance formula) gives us for the distance between 2 points (x1, y1) and (x2, y2) :
distance² = (x1 - x2)² + (y1 - y2)²
in our case
distance² = (20 - 0)² + (-21 - 0)² = 400 + 441 = 841
distance = radius = 29
remember, sine is the up/down leg, cosine is the left/right leg.
so,
sin(theta) = -21/29
FYI : theta ≈ -46.4°
cos(theta) = 20/29
tan(theta) = sin(theta)/cos(theta) = -21/29 / 20/29 =
= -21/20
you were right about tan(theta), not about sin(theta) and cos(theta).
if you mistook theta for a 0, you were still wrong :
sin(0) = 0, cos(0) = 1.