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

Solution:

Given,

p(21, 28) is on the terminal side of θ

When two rays start from a common point, an angle is formed.

The common point is called the vertex.

An angle is in standard position if the vertex lies at origin and the initial arms lie along the positive x-axis.

As the terminal side passes through p(21, 28)

Terminal arm lies in the I quadrant.

The ratio of the opposite side to the hypotenuse side is called the sine.

From the triangle we know that,

sin θ = Opposite/Hypotenuse

Sinθ = y/r

Calculate r,

r = √21² + 28²

r = √441 + 784

r = √1225

r = 35.

Calculate sine,

Sinθ = 28/35

Sinθ = 4/5

Therefore, sinθ = 4/5.

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

Summary:

The point p(21, 28) is on the terminal side of θ. Sinθ = 4/5.