Precalculus : Evaluating Trig Functions
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Example Question #2 : Find The Degree Measure Of An Angle For Which The Value Of A Trigonometric Function Is Known
Which of the following could be a value of 
Which of the following could be a value of 
To begin, it will be helpful to recall the following property of tangent:
This means that if 
The only place where we will have equal values for sine and cosine will be at the locations halfway between our quadrantal angles (axes). In other words, our answer will align with one of the 
Additionally, because our sine and cosine must have opposite signs (one negative and one positive), we need to be in either quadrant 2 or quadrant 4. There is only answer from either of those two, so our answer must be 
Example Question #1 : Find The Degree Measure Of An Angle For Which The Value Of A Trigonometric Function Is Known
Find 
Since we know the value of the trigonometric function and the triangle is located in Quadrant I, we can draw the triangle and get a sense of it. If the opposite side is 1 and the hypotenuse is 2, we know that we're dealing with a 30-60-90 special triangle. And since the opposite side of the angle is 1, we know that the angle is 
Example Question #1 : Find The Degree Measure Of An Angle For Which The Value Of A Trigonometric Function Is Known
Given the equation 
Find 1 possible value of 
Recall that
So if 
Thinking back to our unit circle, recall that cosine corresponds to the x-value. Therefore, we must be in quadrants II or III.
So, which angles correspond to an x-value of -0.5? Well, they must be the angles closest to the y-axis, which are our 
This means our angle must be either
or
It must be 
Note that there are technically infinte solutions, because we are not given a specific interval. However, we only need to worry about one.
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