Download Reference Angles Notes

Trigonometry Unit 1
Topics in Trigonometry
Reference Angles
Reference Angles
• Associated with every angle drawn in the standard
position (except quadrantal angles) there is
another angle called the reference angle.
angle
• The reference angle is the positive
acute angle formed by the terminal
side of the given angle and the x-axis
x axis.
axis.
• Reference angles may appear in
all four quadrants.
• Angles in quadrant I are their
own reference angles.
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Trigonometry Unit 1
Topics in Trigonometry
Remember:
Remember: The reference angle is measured
from the terminal side to the x-axis.
x axis.
(NOT THE Y-AXIS!)
Y AXIS!)
Remember:
Remember: The reference angle is measured
from the terminal side to the x-axis.
x axis.
(NOT THE Y-AXIS!)
Y AXIS!)
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Trigonometry Unit 1
Topics in Trigonometry
Remember:
Remember: The reference angle is measured
from the terminal side to the x-axis.
x axis.
(NOT THE Y-AXIS!)
Y AXIS!)
Remember:
Remember: The reference angle is measured
from the terminal side to the x-axis.
x axis.
(NOT THE Y-AXIS!)
Y AXIS!)
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Trigonometry Unit 1
Topics in Trigonometry
Examples of
Reference Angles
Examples: Draw each angle in standard
position and identify the reference angle.
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Trigonometry Unit 1
Topics in Trigonometry
Examples: Draw each angle in standard
position and identify the reference angle.
5. Write cos 280º as a function of a
positive acute angle. (Multiple Choice)
a) cos 10° b) cos 80° c) cos 85°
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Trigonometry Unit 1
Topics in Trigonometry
6. The value of cos 390º is equal to
which of the following?
a) sin 30° b) sin 60° c) -sin 30°
6. Write tan (-110º) as a function of a
positive acute angle. (Multiple Choice)
a) tan 10° b) tan 20° c) tan 70°
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Trigonometry Unit 1
Topics in Trigonometry
More Examples of
Reference Angles
1. For each indicated value and
quadrant, find the angle measure to the
nearest degree, on the interval [0,360).
(Always use the positive ratio measure when putting into calculator.)
tanθ = −4.7047 Quadrant II
102°
cos θ = 0.9816 Quadrant IV
349°
sin θ = −0.2756 Quadrant IV
344°
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Trigonometry Unit 1
Topics in Trigonometry
Finding Exact Values of Trigonometric Functions
2. Find the exact value of each expression:
sin 300°
Step 1: Sketch the angle and determine
the measure of the reference angle.
sin 60°
Finding Exact Values of Trigonometric Functions
2. Find the exact value of each expression:
sin 300°
Step 2: Determine the sign of the
function (positive or negative).
sin 300°
sin 60°
− sin 60°
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Trigonometry Unit 1
Topics in Trigonometry
Finding Exact Values of Trigonometric Functions
2. Find the exact value of each expression:
sin 300°
Step 3: Evaluate the function.
[Use special right triangles or the
unit circle]
− sin 60°
3
=−
2
3. Find the exact value of each expression:
cos 135°
cos 45°
− cos 45°
=−
2
2
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Trigonometry Unit 1
Topics in Trigonometry
4. Find the exact value of each expression:
tan 240 °
tan 60°
+ tan 60°
= 3
5. Find the exact value of each expression:
sin( −135)°
sin 45°
− sin 45°
=−
2
2
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