SOLUTION: express sec -123 degrees as the same function of a positive acute angle.

Question 34073: express sec -123 degrees as the same function of a positive acute angle.
Answer by kietra(57) (Show Source): You can put this solution on YOUR website!
To express sec -123 degrees as the same function of a positive acute angle, you first need to find a reference angle. In this case it will also be easier to make the angle positive by adding 360 degrees. The trig functions repeat themselves- they are periodic. So, draw a rough sketch of the ange on the coordinate plane and find out which quadrant you are in. Remember that quadrant I is on the upper right and it goes counterclockwise. Here are the rules for finding a reference angle:
Quadrant II: (91-179 degrees) Use the formula 180 - a.
Quadrant III: (181-269 degrees)Use the formula a - 180.
Quadrant IV:(271-359 degrees)Use the formula 360 - a.
Another thing to remember for trig functions are the signs. All six functions are positive in QI, Sine and Cosecant are positive in Q II, Tan and Cotangent are positive in QIII, while Cosine and Secant are positive in Quad IV. I know that�s a mouthful! But, if your angle falls in a quadrant that is negative for your function, you must add a negative sign. In this case, cosine is negative in the second quadrant so our answer will have a negative sign.
So, in your case, you want sec -123 degrees. Convert to positive degrees giving sec 237, From our sketch, we would be in Quadrant 3. So, use 237 - 180 = 57. So our reference angle would be 57 degrees. Secant is negative in the 3rd quadrant so the sign is fine.
-sec 57 degrees

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