you have
x = -20
y = 21
r = 29
sinθ = y/r = 21/29
If θ is an angle in standard position and its terminal side passes through the point (-20,21), find the exact value of \sin\thetasinθ in simplest radical form.
2 answers
I assume you want to find sinθ?
We know that sinθ = opposite/hypotenuse and that our coordinate point is in Quadrant II. If we construct a right triangle with a height of 21 units and a length of 20 units from right to left, then the side opposite of θ is 21 and the side adjacent to θ is -20. We need to determine the hypotenuse, which can easily be solved with the Pythagorean Theorem:
opp^2 + adj^2 = hyp^2
21^2 + (-20)^2 = hyp^2
441 + 400 = hyp^2
841 = hyp^2
29 = hyp
Therefore, sinθ=21/29
We know that sinθ = opposite/hypotenuse and that our coordinate point is in Quadrant II. If we construct a right triangle with a height of 21 units and a length of 20 units from right to left, then the side opposite of θ is 21 and the side adjacent to θ is -20. We need to determine the hypotenuse, which can easily be solved with the Pythagorean Theorem:
opp^2 + adj^2 = hyp^2
21^2 + (-20)^2 = hyp^2
441 + 400 = hyp^2
841 = hyp^2
29 = hyp
Therefore, sinθ=21/29