Question 451756: how do i find the exact value of each trigonometric function using the unit circle?
1. tan225
how do i use a reference angle to find the exact value of the sine, cosine, and tangent of each angle?
1.150
2.-225
3.-300
4.11(pie symbol)/6
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! how do i find the exact value of each trigonometric function using the unit circle?
1. tan225
how do i use a reference angle to find the exact value of the sine, cosine, and tangent of each angle?
1.150
2.-225
3.-300
4.11(pie symbol)/6
..
Before starting this problem make sure you understand the definitions of standard angle and reference angle.
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In standard position, the angle to work with is the angle the terminal side makes with the positive positive side of the axis with its vertex at (0,0). The reference angle is an acute angle formed by the x-axis and the terminal side in standard position.
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1.Tan 225=Tan A This means rotating 225º in the positive direction, counter-clockwise, with the terminal side ending in quadrant III, where the reference angle=45º. This is the standard position of the angle. On the unit circle, x=Cos A, y=sin A, and Tan A=x/y. In this case, x=y, at 225º so tan A=x/y=1. Note that this method could be used for any angle where x and y
may not be equal to each other or have the same sign.
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1.150. Rotating 150º in the positive direction places the terminal side in quadrant II where sin is positive and cos negative, resulting in a reference angle of 30º.
sin 30º=1/2
cos 30º=-√3/2
tan 30º=-√3/3
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2.-225. Rotating 225º in the negative direction places the terminal side in quadrant II where sin is positive and cos negative, resulting in a reference angle of 45º.
sin 45º=√2/2
cos 45º=-√2/2
tan 45º=-1
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3.-300. Rotating 300º in the negative direction places the terminal side in quadrant I where sin and cos are positive, resulting in a reference angle of 60º.
sin 60º=√3/2
cos 60º=1/2
tan 60º=√3
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4.11(pie symbol)/6=11π/6 radians
Rotating 11π/6 in the positive direction places the terminal side in quadrant IV where sin is negative and cos positive, resulting in a reference angle of π/6 radians.
sin π/6=-1/2
cos π/6=√3/2
tan π/6=-√3/3
When working with these problems it is helpful to remember sin is positive in the top half and negative in the bottom half of the unit circle. For cos, the right half is positive and the left half negative.
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