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babunello [35]
3 years ago
6

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

Mathematics
2 answers:
Tju [1.3M]3 years ago
5 0

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

MariettaO [177]3 years ago
4 0

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.

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