Solving Trig Equations In A Given Range

[BOAS]

Homework Statement

Solve cos(3θ) = 0.85 in the range 0 ≤ θ ≤ 360°

Homework Equations

The Attempt at a Solution

cos(3θ) = 0.85

3θ = 31.79°

θ = 10.6° (3 s.f)

I have drawn my transformed cos curve, where the full wave completes after 120°, so there are 3 full cycles in my range.

I often make silly mistakes and I'm not sure of the best method to check my results.

Using the symmetry of the curve I have calculated that θ = 10.6°, 109.4°, 130.6°, 229.4°, 250.6°, 349.4°.

So, how do I verify these?

 

[SteamKing]

For what quadrants is the cosine positive?

 

[BOAS]

1 and 4

 

[SteamKing]

Which of your solutions meet this criteria?

 

[tiny-tim]

Hi BOAS!

cos(3θ) = 0.85

3θ = 31.79°

Easier if you write:

cos(3θ) = 0.85

3θ = 2nπ ± 31.79° ​