5.4 MultipleAngle Identities - Amphitheater Public Schools...Solve sinx + sin3x = 0 Express cos4x...
Transcript of 5.4 MultipleAngle Identities - Amphitheater Public Schools...Solve sinx + sin3x = 0 Express cos4x...
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=
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)
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)
5.4 Multiple angles ID comp.notebook February 17, 2016
Jan 199:50 PM
Power Reducing IdentitiesCommon power reducing identities are:
sin2x=
cos2x=
tan2x=
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
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.
5.4 Multiple angles ID comp.notebook February 17, 2016
Jan 199:50 PM
Ex. 6Solve