Trigonometric Functions of General Angles

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7.4 Trigonometric Functions of General Angles
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What if the angle is not acute?
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provided no denominator equals 0.
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y
x
r
(a, b)
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Find the exact value of each of the six
trigonometric functions of a positive angle
if (-2, 3) is a point on the terminal side.
y
(-2, 3)
x
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y
x
P (1, 0)
P (a, b)
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y
P (0,1)
x
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y
a gt 0, b gt 0, r gt 0
a lt 0, b gt 0, r gt 0
x
r
(a, b)
a lt 0, b lt 0, r gt 0
a gt 0, b lt 0, r gt 0
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y
I (, )
All positive
x
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y
I (, )
All (All functions)
Students ( Sin )
x
Take ( Tangent )
Care ( Cosine )
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Two angles in standard position are said to be
co-terminal if they have the same terminal side.
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y
x
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Let denote a non-acute angle that lies in a
quadrant. The acute angle formed by the terminal
side of and either the positive x-axis or
the negative x-axis is called the reference angle
for
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Reference Angle
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Finding the reference angle

1. Determine the quadrant in which the terminal
   side of the angle formed by the angle lies.

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y
or
x
or
or
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Theorem Reference Angles
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Find the exact value of each of the following
trigonometric functions using reference angles
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