SOLUTION: If cos of theta is -sqrt 3/2 and theta is in quadrant 2, then find the exact values of the other five trigonometric functions. I don't really understand how to do this. If you c

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Question 537064: If cos of theta is -sqrt 3/2 and theta is in quadrant 2, then find the exact values of the other five trigonometric functions.
I don't really understand how to do this. If you can explain the problem step by step, it would be great.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the easiest way to solve this is to look at the cosine of the angle as if the angle was in quad 1.
in that case the cosine would be positive.
you either will know that sqrt(3)/2 is the sine of 60 degrees and is also the cosine of 30 degrees or you can use your calculator to figure it out by finding the arc cosine of sqrt(3)/2.
you will find that the angle (theta) is equal to 30 degrees in quad 1.
this is the angle in quad 1 or the reference angle if in any other quad.
in quad 2, this becomes the reference angle, so you need to take 180 degrees minus 30 degrees to get an equivalent angle of 150 degrees.
that's the angle in quad 2 that has a cosine of minus sqrt(3)/2.
once you know the angle, then the rest is easy.
you should know that the sine of 30 degrees is 1/2.
you should also know that in the graphing of an angle, the hypotenuse is usually set at 1.
this means that the cosine of the angle is always the horizontal side and the sine of the angle is always the vertical side of the triangle formed.
you can figure out the rest of the trigonometric functions by just using the definitions.
use the reference angle in quad 2 to determine the other values.
the reference angle is 30 degrees.
the equivalent angle is 150 degrees.
in quad 2:
sine is positive
cosine is negative
tangent is negative
cotangent is reciprocal of tangent
secant is reciprocal of cosine
cosecant is reciprocal of sine
see the attached pictures for the value as calculated there.
we are working with sine = 1/2 and cosine = -sqrt(3)/2