document.write( "Question 34073: express sec -123 degrees as the same function of a positive acute angle. \n" ); document.write( "

Algebra.Com's Answer #20537 by kietra(57) $\"\"$ $\"About$

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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:
\n" ); document.write( "Quadrant II: (91-179 degrees) Use the formula 180 - a.
\n" ); document.write( "Quadrant III: (181-269 degrees)Use the formula a - 180.
\n" ); document.write( "Quadrant IV:(271-359 degrees)Use the formula 360 - a.
\n" ); document.write( "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. \r
\n" ); document.write( "\n" ); document.write( "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.
\n" ); document.write( "-sec 57 degrees
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