Question

Solve. Give the answers in degrees so that 0° ≤ θ < 360°.

1) (5 cos θ - 1) / 2 = 1
answers: 53°, 127°, 233°

2) 3 cot (2θ) + 3 = 0

3) tan^2 θ + 2 sec^2 θ = 3

is my answer for #1 correct and i'm not sure how to do #2 and #3.

Answer 1

is the answer to #3 39°?

Answer 2

#3 trick is to get sin^2 + cos^2 = 1 in there

sin^2/cos^2 + 2 /cos^2 = 3

sin^2 + 2 = 3 cos^2


sin^2 + cos^2 + 2 = 4 cos^2

1 + 2 = 4 cos^2

cos^2 = .75

cos = .866

then theta = 30 degrees

Answer 3

#2
3 cot (2θ) + 3 = 0
cot(2Ø) = -1
tan(2Ø)= -1
we know tan is negative in II or IV
the reference angle is 45°
that is, we know tan 45° = +1

so 2Ø = 180-45 or 2Ø = 360-45
2Ø = 135° or 2Ø = 315°
Ø = 67.5° or Ø = 157.5°

we also know that the period of tan 2Ø is 90°

so we can add/subtract 90° to get more answers
Ø = 157.5+90 = 247.5
Ø = 247.5+90 = 337.5°

As you can see you will have 4 anwers.