Precalc 4.4 Notes.notebook
Sec. 4.4
Precalculus
Trig. Functions of Any Angle
­ in section 3 we used the trig. functions dealing with acute angles
­ in section 2 we used the unit circle to evaluate the trig functions
­ in this section we will combine these ideas to find the value of the trig functions of any angle
Steps
­ draw the angle (start on positive x­axis), vertex at the origin
­ from the end of the angle, draw a line perpendicular to the x­axis
­ the angle formed by the 'radius' and the x­axis is called the reference angle.
­ use pythagorean theorem to find the third side
­ use the reference angle to find the values of the trig functions
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Precalc 4.4 Notes.notebook
Example
Determine the exact values of the 6 trig functions of the angle θ
(­5,6)
θ
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Precalc 4.4 Notes.notebook
Example
The point (6,­4) is on the terminal side of the angle in standard position. Determine the exact values of the six trig functions of the angle.
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Precalc 4.4 Notes.notebook
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Precalc 4.4 Notes.notebook
Example
Find the values of the six trig functions of θ, if you know
and lies in the third quadrant. 5
Precalc 4.4 Notes.notebook
Example
Without using a calculator find the exact value of the sine, cosine and tangent of 390 degrees.
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Precalc 4.4 Notes.notebook
Example
Without using a calculator find two solutions of the equation
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