Question

Use the unit circle to find the value of sin 3π/2 and cos 3π/2. Show work please!

Answer 1

Explanation:

3π/2 is equivalent to 270°. The "opposite side" for this angle is -2; the adjacent side is 0, and the hypotenuse is 2.

Thus, sin 3π/2 = opp/hyp = -2/2 = -1, and

cos 3π/2 = adj/hyp = 0/2 = 0.

Answer 2

`sin(3\pi)/(2)=-1` and
`cos(3\pi)/(2)=0`

Explanation:

We are given that a unit circle

We have to find the value of
`sin(3\pi)/(2)` and
`cos(3\pi)/(2)` by using the unit circle

Radius of circle=r=1 unit

We know that

`x=r cos\theta` and
`y=r sin\theta`

We
`\theta=(3\pi)/(2)`

Then x=
`1\cdot cos(3\pi)/(2)`

`x=cos (2\pi-(\pi)/(2))`

`x=cos (\pi)/(2)` (
`cos(2\pi-\theta)=cos\theta`)

`x=0 (cos(\pi)/(2)=0)`

`y=1\cdot sin(3\pi)/(2)`

`y=sin(2\pi-(\pi)/(2))`

`y=-sin(\pi)/(2)` (
`sin(2\pi-\theta)=-sin\theta`)

`y=-1` (
`sin(\pi)/(2)=1`)

Hence,
`sin(3\pi)/(2)=-1` and
`cos(3\pi)/(2)=0`