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

1.Solve sin(x)=−0.61sin(x)=-0.61 on 0≤x<2π0≤x<2πThere are
two solutions, A and B, with A < B
2.Solve 5cos(5x)=25cos(5x)=2 for the smallest three positive
solutions.Give your answers accurate to at least two decimal
places, as a list separated by commas
3.Solve 5sin(π4x)=35sin(π4x)=3 for the four smallest positive
solutions
4.Solve for tt, 0≤t<2π0≤t<2π
21sin(t)cos(t)=9sin(t)21sin(t)cos(t)=9sin(t)
5.Solve for the exact solutions in the interval [0,2π)[0,2π). If
the equation has no solutions, respond with DNE.
2sec2(x)=3−tan(x)
6.Give the smallest two solutions of sin(7θθ) = -0.6942 on [...

Solve 8cos2(x)+2cos(x)−3=08cos2(x)+2cos(x)-3=0 for all solutions
0≤x<2π0≤x<2π
and
Solve 6sin2(w)−cos(w)−5=06sin2(w)-cos(w)-5=0 for all solutions
0≤w<2π0≤w<2π

1, Solve cos(x)=0.17cos(x)=0.17 on 0≤x<2π0≤x<2π
There are two solutions, A and B, with A < B
2, Find the EXACT value of cos(A−B)cos(A-B) if sin A = 3434, cos
A = √7474, sin B = √91109110, and cos B = 310310.
cos(A−B)cos(A-B) =
3,
Find all solutions of the equation 2cosx−1=02cosx-1=0 on
0≤x<2π0≤x<2π
The answers are A and B, where A<BA<B
A=? B=?

Find all solutions to 2 cos t = 0.35 for 0 ≤ t ≤ 2π Give
answers correct to 3 decimal places. Give answers in degrees.

Find all exact solutions on the interval
0 ≤ x < 2π.
(Enter your answers as a comma-separated list.)
cot(x) + 4 = 5
x=

Solve 6cos2(t)+sin(t)−4=06cos2(t)+sin(t)-4=0 for all solutions
0≤t<2π0≤t<2π

For the following exercises, find all exact solutions on [0,
2π)
23. sec(x)sin(x) − 2sin(x) = 0
25. 2cos^2 t + cos(t) = 1
31. 8sin^2 (x) + 6sin(x) + 1 = 0
32. 2cos(π/5 θ) = √3

1.Find all solutions on the interval [0, 2π)
csc (2x)-9=0
2. Rewrite in terms of sin(x) and cos(x)
Sin (x +11pi/6)

Solve
5cos(2x)=5cos2(x)−15cos(2x)=5cos2(x)-1
for all solutions 0≤ x <2π

Find all solutions of the equation. (Enter all answers including
repetitions. Enter your answers as a comma-separated list.)
x4 + 5x3− 17x2− 15x
+ 42 = 0
Find all solutions of the equation. (Enter
all
answers including repetitions. Enter your
answers as a comma-separated list.)
6x5 + 43x4 + 37x3 − 30x2 = 0
Find all solutions of the equation. (Enter
all answers including repetitions. Enter your answers as a
comma-separated list.)
x3 − 8x2 − 19x − 10...

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