Question

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

Answer 1

Answer:

$sin\frac{3\pi}{2}=-1$ and $cos\frac{3\pi}{2}=0$

Step-by-step explanation:

We are given that a unit circle

We have to find the value of $sin\frac{3\pi}{2}$ and $cos\frac{3\pi}{2}$ by using the unit circle

Radius of  circle=r=1 unit

We know that

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

We $\theta=\frac{3\pi}{2}$

Then x=$1\cdot cos\frac{3\pi}{2}$

$x=cos (2\pi-\frac{\pi}{2})$

$x=cos \frac{\pi}{2}$  ($cos(2\pi-\theta)=cos\theta$)

$x=0 (cos\frac{\pi}{2}=0)$

$y=1\cdot sin\frac{3\pi}{2}$

$y=sin(2\pi-\frac{\pi}{2})$

$y=-sin\frac{\pi}{2}$  ($sin(2\pi-\theta)=-sin\theta$)

$y=-1$   ($sin\frac{\pi}{2}=1$)

Hence, $sin\frac{3\pi}{2}=-1$ and $cos\frac{3\pi}{2}=0$

Answer 2

Answer:

Step-by-step 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.