Use Reference Angles to Evaluate Functions For Dummies

Evaluating Trig Functions Step 1 Find the reference angle and graph it

sin380° Step one find reference angle and graph. Take to get 20° for reference angle and then step one is complete

Evaluating Trig Functions Step 2 Evaluate Trig function using reference angle Quadrant One (I)Quadrant Two (II) Quadrant Four (IV)Quadrant Three (III)

20° was the reference angle and it is in quadrant one. The function was sine, so take sine of 20° The sine of 20° is So that is the answer the problem, if the function is in the right quadrant.

Evaluating Trig Functions Step 3 Change the sign if necessary. If the original angle you graphed lied in a quadrant with a different trig function than you were given, it is going to be negative. Before your answer is complete put negative signs in front of the degrees and radians that you came up with.

Quadrants Explained Quadrant One If the original angle you graphed fell into quadrant one it will ALWAYS be positive for every trig function. A function, sine, cosine, tangent, cosecant, secant, or cotangent, regardless will be given, and all will be positive in the first quadrant. Quadrant One (I)

All trig functions positive in quadrant one 20°

Quadrants Explained Quadrant Two If the original angle you graphed fell into the second quadrant. It will only be positive if the trig function you were given with it was sine or cosecant. All other trig functions given with a reference angle that lies in the second quadrant will be negative. Quadrant Two (II)

Sine and Cosecant are positive in quadrant two 130°

Quadrants Explained Quadrant Three If the original angle you graphed fell into the third quadrant. It will only be positive if the trig function you were given with it was tangent or cotangent. All other trig functions given with a reference angle that lies in the third quadrant will be negative. Quadrant Three (III)

Tangent and Cotangent are positive in quadrant 3 220°

Quadrants Explained Quadrant Four If the original angle you graphed fell into the fourth quadrant. It will only be positive if the trig function you were given with it was cosine or secant. All other trig functions given with a reference angle that lies in the fourth quadrant will be negative. Quadrant Four (IV)

310° Cosine and Secant are positive in quadrant 4

Step by Step sec135 Step 1: Take to get reference angle and graph it = 45°

Step by Step sec135

Independent problem tan(-500°) Solve

Independent problem tan(-500°)

Step 2: Evaluate the trig function using the reference angle Take tan40 tan40=.839

Independent problem tan(-500°) Step 3: Change sign if necessary Since the original angle fell in the third quadrant, and tangent is positive in the third quadrant, the sign stays positive. So… Tan(-500)=.839

Tricks to Remembering Chart can be used instead of calculator working out functions if you have “nice angles”, or the ones found in the chart Just because the angle given is negative doesn’t mean that the answer will be negative