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5.5 Multiple-Angle Formulas. Students will use multiple-angle formulas to rewrite and evaluate trigonometric functions. Students will use power-reducing formulas to rewrite and evaluate trigonometric functions. - PowerPoint PPT Presentation
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5.5 Multiple-Angle Formulas
Students will use multiple-angle formulas to rewrite and evaluate trigonometric functions.
Students will use power-reducing formulas to rewrite and evaluate trigonometric functions.
Students will use half-angle formulas to rewrite and evaluate trigonometric functions.
Students will use product-to-sum and sum-to-product formulas to rewrite and evaluate trigonometric functions.
Section 5.5, Double-Angle Formulas, pg. 375
Why is ?
Remember:
sin sin cos2 2 sin( ) sin cos cos sina b a b a b
Example 1
2 2 0cos sin Solve.
Try #10 on p. 382
Why is ?
Remember:
cos cos sin2 2 2 cos( ) cos cos sin sina b a b a b
Example 3Use the following to find and : sin 2 cos2 tan 2
sin 2
cos2
tan 2
cos 5
133
22
Try #18 on p. 382
Section 5.5, Half-Angle Formulas, pg. 378
Use the figure (p.382 #33-40) to find the exact value of the trigonometric function.
cos2
Try #34 on p. 382
Example 6
Find the exact value of sin105
Try #42 on p. 383
Find the following values given in quad. II sin
2
cos2
tan2
sin 5
13
Try #50 on p. 383
Use the half-angle formulas to simplify the expression.
1 6
2
cos x
Try #56 on p. 383
Example 7
Find all solutions if in the interval
2 22
2 2 sin cos [ , )0 2
Section 5.5, Product-to-Sum Formulas, pg. 379
Example 8 Rewrite the product as a sum or differencecos sin5 4
Section 5.5, Sum-to-Product Formulas, pg. 380
Example 9
Find the exact value of cos cos195 105
Example 10
Find all solutions of in the interval sin sin5 3 0x x [ , )0 2
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