Answer to Question #91661 in Trigonometry for Haley Lucas

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)

"\\sin\\alpha=\\frac{opposite}{hypotenuse}"

"\\sin\\alpha=\\frac{BC}{AB}"

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

Then:

"\\sin\\alpha=\\frac{y}{1}""\\sin\\alpha=y"

(c)

"\\cos\\alpha=\\frac{adjacent}{hypotenuse}"

"\\cos\\alpha=\\frac{AC}{AB}"

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


"\\cos\\alpha=x"

At the point where

"\\alpha=\\frac{3\\pi}{2}""x=0"

According to this,

"\\cos\\frac{3\\pi}{2}=0"

"y=-1"

And that is why

"\\sin\\frac{3\\pi}{2}=-1"

Answer:

"\\sin\\frac{3\\pi}{2}=-1"

"\\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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