Question #91661
Use the unit circle to find the value of sin 3(pi)/2 and cos 3(pi)/2
1
Expert's answer
2019-07-17T08:59:23-0400

Solution.

(a)x2+y2=1

This is the equation of unit circle,where radius equals 1.

Let us consider the right triangle ABC.Hypotenuse AB is radius itself.As long as R=1,AB=1.

(b)

sinα=oppositehypotenuse\sin\alpha=\frac{opposite}{hypotenuse}

sinα=BCAB\sin\alpha=\frac{BC}{AB}

BC is AB projection on y-axis,so that BC=y.

Then:

sinα=y1\sin\alpha=\frac{y}{1}sinα=y\sin\alpha=y

(c)

cosα=adjacenthypotenuse\cos\alpha=\frac{adjacent}{hypotenuse}

cosα=ACAB\cos\alpha=\frac{AC}{AB}

AC is AB projection on x-axis,so that AC=x.Then:


cosα=x\cos\alpha=x

At the point where

α=3π2\alpha=\frac{3\pi}{2}x=0x=0

According to this,

cos3π2=0\cos\frac{3\pi}{2}=0

y=1y=-1

And that is why

sin3π2=1\sin\frac{3\pi}{2}=-1

Answer:

sin3π2=1\sin\frac{3\pi}{2}=-1

cos3π2=0\cos\frac{3\pi}{2}=0


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Comments

Rupinder kaur
14.07.19, 11:36

Firstly notice that you can plot a point on a circle using coordinate, (cosx, sinx). Here the point (cos3 pi/2,sin3 pi/2) is the point (0,-1) on the unit circle.

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