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# I need a little help

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If sine of Theta=0.4, what is the value of cosine of Theta?

Guest Dec 9, 2015

#2
+92751
+10

That is a really good answer Will85237

I'll show you another approach :)

If sine of Theta=0.4, what is the value of cosine of Theta?

0.4= 2/5

Draw a right angled triangle and label one of the acute angles as theta.

sine theta = 2/5

so mark the opposite side as 2 and the hypotenuse as 5

The adjacent side will be sqrt(25-4) = sqrt(21)

So cos(theta) = sqrt(21)/5 = sqrt(0.84)    which is exactly what Will found.

Theta could also be  in  the 2nd quadrant. In this case cos(theta) = -sqrt(21)/5

Melody  Dec 10, 2015
#1
+555
+5

Use the following trigonometric identity.

$$sin^2(\theta )+cos^2(\theta )=1$$

Rearrange it in terms of cos.

$$cos(\theta )=\sqrt{1-sin^2(\theta )}$$

Substitute in your value of sine of theta, 0.4.

$$cos(\theta )=\sqrt{1-0.4^2}$$

Solve.

$$cos(\theta )=\sqrt{1-0.16}$$

$$cos(\theta )=\sqrt{0.84}$$

As an approximation.

$$cos(\theta )=0.92$$

Will85237  Dec 9, 2015
#2
+92751
+10

That is a really good answer Will85237

I'll show you another approach :)

If sine of Theta=0.4, what is the value of cosine of Theta?

0.4= 2/5

Draw a right angled triangle and label one of the acute angles as theta.

sine theta = 2/5

so mark the opposite side as 2 and the hypotenuse as 5

The adjacent side will be sqrt(25-4) = sqrt(21)

So cos(theta) = sqrt(21)/5 = sqrt(0.84)    which is exactly what Will found.

Theta could also be  in  the 2nd quadrant. In this case cos(theta) = -sqrt(21)/5

Melody  Dec 10, 2015