5.4 MultipleAngle Identities - Amphitheater Public Schools...Solve sinx + sin3x = 0 Express cos4x...

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5.4 Multiple angles ID comp.notebook February 17, 2016 Jan 199:50 PM 5.4 MultipleAngle Identities There are several double angle formulae that we need to know: sin2x= cos2x= tan2x=

Transcript of 5.4 MultipleAngle Identities - Amphitheater Public Schools...Solve sinx + sin3x = 0 Express cos4x...

Page 1: 5.4 MultipleAngle Identities - Amphitheater Public Schools...Solve sinx + sin3x = 0 Express cos4x using double angles. TRY with a little help :) Solve cos2x + cos4x = 0 on [0,2π)

5.4 Multiple angles ID comp.notebook February 17, 2016

Jan 19­9:50 PM

5.4 Multiple­Angle Identities

There are several double angle formulae that we need to know:

sin2x=

cos2x=

tan2x=

Page 2: 5.4 MultipleAngle Identities - Amphitheater Public Schools...Solve sinx + sin3x = 0 Express cos4x using double angles. TRY with a little help :) Solve cos2x + cos4x = 0 on [0,2π)

5.4 Multiple angles ID comp.notebook February 17, 2016

Jan 19­9:50 PM

Ex. 1Prove cos2x = cos2x ­ sin2x

Ex. 2Solve cos2x=sinx on [0,2 π)

TRYSolve sin2x=2sinx on [0,2π)

Page 3: 5.4 MultipleAngle Identities - Amphitheater Public Schools...Solve sinx + sin3x = 0 Express cos4x using double angles. TRY with a little help :) Solve cos2x + cos4x = 0 on [0,2π)

5.4 Multiple angles ID comp.notebook February 17, 2016

Jan 19­9:50 PM

Ex. 3Solve sinx + sin3x = 0

Express cos4x using double angles. 

TRY ­ with a little help :)

Solve cos2x + cos4x = 0 on [0,2π)

Page 4: 5.4 MultipleAngle Identities - Amphitheater Public Schools...Solve sinx + sin3x = 0 Express cos4x using double angles. TRY with a little help :) Solve cos2x + cos4x = 0 on [0,2π)

5.4 Multiple angles ID comp.notebook February 17, 2016

Jan 19­9:50 PM

Power Reducing IdentitiesCommon power reducing identities are:

sin2x=

cos2x=

tan2x=

Page 5: 5.4 MultipleAngle Identities - Amphitheater Public Schools...Solve sinx + sin3x = 0 Express cos4x using double angles. TRY with a little help :) Solve cos2x + cos4x = 0 on [0,2π)

5.4 Multiple angles ID comp.notebook February 17, 2016

Jan 19­9:50 PM

Ex. 4With the aid of the power reducing identities prove that 

Page 6: 5.4 MultipleAngle Identities - Amphitheater Public Schools...Solve sinx + sin3x = 0 Express cos4x using double angles. TRY with a little help :) Solve cos2x + cos4x = 0 on [0,2π)

5.4 Multiple angles ID comp.notebook February 17, 2016

Jan 19­9:50 PM

Half­Angle identitiesAnother set of useful identities are:

Ex. 5

Evaluate cos 15o without a calculator.

Page 7: 5.4 MultipleAngle Identities - Amphitheater Public Schools...Solve sinx + sin3x = 0 Express cos4x using double angles. TRY with a little help :) Solve cos2x + cos4x = 0 on [0,2π)

5.4 Multiple angles ID comp.notebook February 17, 2016

Jan 19­9:50 PM

Ex. 6Solve