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7.4 Trigonometric Functions of General Angles

What if the angle is not acute?

provided no denominator equals 0.

y

x

r

(a, b)

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

(No Transcript)

y

x

P (1, 0)

P (a, b)

y

P (0,1)

x

(No Transcript)

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

y

I (, )

All positive

x

y

I (, )

All (All functions)

Students ( Sin )

x

Take ( Tangent )

Care ( Cosine )

Two angles in standard position are said to be

co-terminal if they have the same terminal side.

y

x

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

Reference Angle

Finding the reference angle

- Determine the quadrant in which the terminal

side of the angle formed by the angle lies.

y

or

x

or

or

Theorem Reference Angles

Find the exact value of each of the following

trigonometric functions using reference angles

(No Transcript)

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