Question

1.Solve 3cos(2α)=3cos2(α)−23cos(2α)=3cos2(α)-2 for all solutions on the interval 0≤α<2π0≤α<2π

αα =    

Give your answers accurate to at least 3 decimal places, as a list separated by commas

2.Solve 7sin(2w)−5cos(w)=07sin(2w)-5cos(w)=0 for all solutions on the interval 0≤w<2π0≤w<2π

ww =    

Give your exact solutions if appropriate, or solutions accurate to at least 3 decimal places, as a list separated by commas

3.Solve 7sin(2β)−2cos(β)=07sin(2β)-2cos(β)=0 for all solutions 0≤β<2π0≤β<2π

ββ =    

Give exact answers or answers accurate to 3 decimal places, as appropriate

4.Solve 2cos2(w)−cos(w)−1=02cos2(w)-cos(w)-1=0 for all solutions.

Your initial angle should be between 0 and 2π2π (not including 2π2π, and your initial angles should go from least to greatest. Consider 2nπ2nπ to have an initial angle of 0). Use nn as your multiplier.

w =    

w =    

w =   

5.Solve 7cos(2θ)=7cos2(θ)−17cos(2θ)=7cos2(θ)-1 for all solutions 0≤θ<2π0≤θ<2π

θθ =    

Give answers accurate to 3 decimal places.

6.Solve sin2(x)=−cos(x)sin2(x)=-cos(x) for all solutions 0≤x<2π0≤x<2π

xx =    

Give your answers accurate to 3 decimal places, as a list separated by commas

7.Solve 6sin2(w)−7cos(w)−8=06sin2(w)-7cos(w)-8=0 for all solutions on the interval 0≤w<2π0≤w<2π

ww =    

Give your answers accurate to at least 3 decimal places, as a list separated by commas

8.Solve 4sin2(x)−9sin(x)−9=04sin2(x)-9sin(x)-9=0 for all solutions 0≤x<2π0≤x<2π

xx =    

Give your answers accurate to at least 3 decimal places, as a list separated by commas

9.Solve 12cos2(t)−13cos(t)+3=012cos2(t)-13cos(t)+3=0 for all solutions 0≤t<2π0≤t<2π

tt =    

Give your answers accurate to at least 3 decimal places, as a list separated by commas

10. Solve 2sin2(w)+3sin(w)+1=02sin2(w)+3sin(w)+1=0 for all solutions on the interval 0≤w<2π0≤w<2π. Your solutions must be exact, that is, in terms of ππ.

ww =    

Answer 1