Question

The point P(15, 20) is on the terminal side of θ. Evaluate sin θ.

Option 1: Four fifths
Option 2: Four thirds
Option 3: Three fifths
Option 4: Three fourths

Answer 1

To find sinθ for point P(15, 20), calculate the hypotenuse using the Pythagorean theorem, then divide the y-coordinate by the hypotenuse. The correct evaluation is 4/5.

Step-by-step explanation:

To evaluate sinθ for the point P(15, 20) which lies on the terminal side of angle θ, we first consider the right triangle formed by drawing a perpendicular from P to the x-axis. The x-coordinate represents the adjacent side, the y-coordinate represents the opposite side, and the hypotenuse can be found using the Pythagorean theorem.

The hypotenuse (r) is:
√(15² + 20²) = √(225 + 400) = √625 = 25.

Now, using the definition of sine, which is the opposite over hypotenuse :
sinθ = 20 / 25 = 4/5.