Question

Find the exact value of sin3π2 . A. −23√3 B. −1 C. 3√2 D. 0

Answer 1

The best way to answer this question is by taking a look at the Unit Circle:

The Unit Circle is a circle with the radius of 1 that is usually used as a reference when answering problems regarding trigonometry and angle measurements.

The Unit Circle is broken into 4 quadrants, with the first quadrant holding the angles 30, 45, 60 and 90. They can also be written as fractions of π:

• 0°/ 360° = 2π
• 30° = π/6
• 45° = π/4
• 60° = π/3
• 90° = π/2

Sin and Cos on the unit circle are seen in the x and y coordinates of these angles on the unit circle. They are as followed:

• 30° = π/6 = (
  `\frac{\sqrt[]{3} }{2}` ,
  `(1)/(2)` )
• 45° = π/4 = (
  `(√(2) )/(2)`,
  `(√(2) )/(2)` )
• 60° = π/3 = (
  `\frac{\sqrt[]{3} }{2}`,
  `(1)/(2)` )
• 90° = π/2 = (0, 1)

Sin is the y coordinate and cos is the x coordinate.

To find sin3π/2, look at the unit circle. It takes some time to fully memorize the unit circle, so reference it until you are comfortable enough recalling the information.

Find sin 3π/2 on the unit circle and look at the y coordinate to find your answer:

B: -1