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

 Dec 9, 2015

Best Answer 

 #2
avatar+109519 
+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 

 Dec 10, 2015
 #1
avatar+561 
+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.

\(cos(\theta )=0.92\)

.
 Dec 9, 2015
 #2
avatar+109519 
+10
Best Answer

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

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