Use Reference Angles to Evaluate Functions For Dummies

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Evaluating Trig FunctionsStep 1

• Find the reference angle and graph it

sin380°

• Step one find reference angle and graph.• Take 380-360 to get 20° for reference angle

and then step one is complete

Evaluating Trig FunctionsStep 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 0.34. So that is the answer the problem, if the function is in the right quadrant.

Evaluating Trig FunctionsStep 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 ExplainedQuadrant 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 ExplainedQuadrant 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 ExplainedQuadrant 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 ExplainedQuadrant 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 Stepsec135

Step 1: Take 180-135 to get reference angle and graph it180-135= 45°

Step by Stepsec135

• Step 2: Evaluate trig function using reference angle

• Reference angle was 45°• sec45°= • The was found using the chart. Any of the

“nice angle” trig functions can be evaluated using the chart.

Step by Stepsec135

• Step 3: Change sign if necessary. • Since the original angle fell in the second

quadrant, and all the trig functions except for sine and cosecant are negative in the second quadrant, so the answer is negative.

• sec135= -

Independent problemtan(-500°)

• Solve

Independent problemtan(-500°)

• Step one: Find reference angle and graph it.• Even though the angle is negative, you still find the

reference angle as a positive.• Since it is more than a whole circle, you first have to

subtract off a whole circle. • 500-360=140°• Then find the reference angle as usual, so do • So 40° is the reference angle

Independent problemtan(-500°)

• Step 2: Evaluate the trig function using the reference angle

• Take tan40• tan40=.839

Independent problemtan(-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