Determining all values of Θ (gr. 11 math)

[eleventhxhour]

8) Use each trigonometric ratio to determine all values of Θ, to the nearest degree if 0°≤ Θ ≤ 360°.

c) cosΘ = -0.8722

So, this is what I did for this question:
Θ=cos^-1(-0.8722)
Θ = 151°

This is correct, according to the textbook. However, it also gives another answer: 209°. How do you get this using the equations? (like sin (360° - Θ) = -sinΘ, tan (180° + Θ) = tanΘ, etc.)

d) cotΘ = 8.1516.

So, here's what I did for this part:
Θ = 7°
tan(180+7)= 187°
tan(360-7) = 353°

HOWEVER, the textbook only has the answers 7° and 187°. Why wouldn't 353° be correct?

Thanks!

 

[MarkFL]

For part c) consider the identity:

\(\displaystyle \cos\left(360^{\circ}-\theta\right)=\cos(\theta)\)

For part d), you are essentially trying to assert that:

\(\displaystyle \tan(-\theta)=\tan(\theta)\)

Is this true?