Question

In a unit circle, ø= 90°. Identify the terminal point and sin Ø.

A. Terminal point: (0,1); sin ø= 1
B. Terminal point: (1,0); sin ø=0 C. Terminal point: (1, 0); sin ø=1
D. Terminal point: (0,1); sin ø=0

Answer 1

Terminal point: (0, 1); sinФ = 1 ⇒ A

Explanation:

In the unit circle, Ф is the angle between the terminal side and the positive part of the x-xis.

• The terminal point on the positive part of the x-axis is (1, 0),which means Ф = 0° or 360° and cosФ = 1, sinФ = 0

• The terminal point on the positive part of the y-axis is (0, 1),which means Ф = 90° and cosФ = 0, sinФ = 1

• The terminal point on the negative part of the x-axis is (-1, 0),which means Ф = 180° and cosФ = -1, sinФ = 0

• The terminal point on the negative part of the y-axis is (0, -1),which means Ф = 270° and cosФ = 0, sinФ = -1

In a unit circle

∵ Ф = 90°

→ By using the 2nd rule above

∴ The terminal point is (0, 1)

∴ sinФ = 1

∴ Terminal point: (0, 1); sinФ = 1