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Solving trigonometric equations II: using identities and quadratic form — Homework
Substitute u for the repeated trig function, solve the resulting quadratic, then convert every u-value back to x.
- 1.Solve 2sin^2(x)-sin(x)-1=0 for x in [0,2pi).
- 2.Solve cos(2x)=cos(x) for x in [0,2pi), using cos(2x)=2cos^2(x)-1.
- 3.Solve 2cos^2(x)-3cos(x)+1=0 for x in [0,2pi).
- 4.Solve sin(2x)+sin(x)=0 for x in [0,2pi), factoring rather than canceling sin(x).
- 5.Explain why letting u=sin(x) or u=cos(x) turns an unfamiliar trig equation into a familiar one, and why you must still convert back to x at the end.
🌲 Homeschool of the FutureTwelfth Grade · Math · week 26 homework