Question 404420: Express each as a function of theta :
a. sin (270degrees + theta )
b.cos ( pi + theta )
c.tan (810degrees + theta )
d.sin ( theta - 180 )
thanks for any help
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Express each as a function of theta :
a. sin (270degrees + theta )
b.cos ( pi + theta )
c.tan (810degrees + theta )
d.sin ( theta - 180 )
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To understand the following solutions, you must be familiar with the unit circle in which we will determine the reference angle and the quadrant it is in. The reference angle is always formed by the x-axis and the rotated terminal side.
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a. sin (270degrees + theta )
Rotating counter-clockwise 270 deg + acute angle, theta. You are in the 4th quadrant with the reference angle=90-theta. Since the sin function in the 4th quadrant is negative, solution: -sin(90-theta)or cos (theta)
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b.cos ( pi + theta )
Rotating counter-clockwise 180 deg + acute angle, theta. This puts the reference angle in the third quadrant where the cos is negative. Solution: -cos(theta)
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c.tan (810degrees + theta )
Rotating counter-clockwise 720 deg (twice around) + 90 deg.This puts the reference angle right on 90 deg. Solution: tan 90 deg (which is undefined)
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d.sin ( theta - 180 )
This says to rotate counter-clockwise acute angle theta, then rotate clockwise 180 degrees. This puts the reference angle = theta in the 3rd quadrant where sin function is negative. Solution: -sin (theta)
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Hope this helps. It would have been much easier to explain with diagrams.
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