Question

The point p(21, 28) is on the terminal side of θ. evaluate sin θ.

Answer 1

To evaluate sin θ, use a right triangle formed by the given point and the origin. Find the length of the hypotenuse using the Pythagorean theorem and then evaluate sin θ by dividing the opposite side length by the hypotenuse.

Step-by-step explanation:

To evaluate sin θ, we need to find the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle. Since the point (21, 28) is on the terminal side of θ, we can form a right triangle with the x-axis as the adjacent side, the y-axis as the opposite side, and the hypotenuse as the distance between the point and the origin. Using the Pythagorean theorem, we can find the length of the hypotenuse:

h = √(21^2 + 28^2) = √(441 + 784) = √1225 = 35

Now we can evaluate sin θ:

sin θ = opposite/hypotenuse = 28/35 ≈ 0.8