Question 723038: 4. a)express tan 322 degrees as a tangent function of a positive acute angle.
b) if (-4,1) is a point on the terminal side of angle theta in standard position, evaluate all six trigonometric functions of theta in simplest radical form.
c) the point (- radical 2/2,radical 2/2) is on the terminal side of angle theta in standard position. If the distance of the point from the origin is one unit, find sin theta and cos theta
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! 4. a)express tan 322 degrees as a tangent function of a positive acute angle.
use reference angle in quadrant IV where tan<0
tan 322º=-tan 38º
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b) if (-4,1) is a point on the terminal side of angle theta in standard position, evaluate all six trigonometric functions of theta in simplest radical form.
You are working with a reference right triangle in quadrant II. Adjacent side=-4. Opposite side=1.
Hypotenuse=√(4^2+1^2)=√(16+1)=√17
sin theta=1/√17
cos theta=-4/√17
tan theta=-1/4
csc theta=√17
sec theta=-√17/4
cot theta=-4
c) the point (- radical 2/2,radical 2/2) is on the terminal side of angle theta in standard position. If the distance of the point from the origin is one unit, find sin theta and cos theta
The working reference right triangle is also in quadrant II where sin>0 and cos<0
In this case the hypotenuse=1
sin theta=√2/2
cos theta=-√2/2
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