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

Question

asked Feb 9, 2020 57.4k views

2 Answers

Jeroen Vervaeke · Answer 1 · 2020-02-10T23:33:15+0000

Answer:

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.

Sebastian Redl · Answer 2 · 2020-02-15T23:27:52+0000

Answer:

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