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# Unit Circle, CAST, Quadrants, Exact Values and Special Triangles (Part 1)

1. 1
Point P(3,4) lies on the terminal arm of $\angle{\theta}$ in standard position. ($0°\leq\theta\leq360°$).

a) Determine the exact values for $\sin\theta$, $\cos\theta$, $\tan\theta$, $\csc\theta$, $\sec\theta$, and $\cot\theta$.

b) Find $\theta$ (to the nearest degree).
2. 2
Point P(-5,12) lies on the terminal arm of $\angle{\theta}$ in standard position. ($0°\leq\theta\leq360°$).

a) Determine the exact values for $\sin\theta$, $\cos\theta$, $\tan\theta$, $\csc\theta$, $\sec\theta$, and $\cot\theta$.

b) Find $\theta$ (to the nearest degree).
3. 3
Point P(-2,-4) lies on the terminal arm of $\angle{\theta}$ in standard position. ($0°\leq\theta\leq360°$).

a) Determine the exact values for $\sin\theta$, $\cos\theta$, $\tan\theta$, $\csc\theta$, $\sec\theta$, and $\cot\theta$.

b) Find $\theta$ (to the nearest degree).
4. 4
A terminal arm is rotated through an angle of 160°.

Determine one possible point on the terminal arm.
5. 5
A terminal arm is rotated through an angle of 150°.

Determine one possible point on the terminal arm.
6. 6
A terminal arm is rotated through an angle of 240°.

Determine one possible point on the terminal arm.
7. 7
Find the exact value of:

a) sin 150°

b) cos 225°
8. 8
Find the exact value of:

a) tan 300°

b) sin 240°
9. 9
Find the exact value of:

a) sin 120°

b) tan 315°
10. 10
Find the exact value for:

a) sin 0°, sin 90°, sin 180°, sin 270° and sin 360°

b) cos 0°, cos 90°, cos 180°, cos 270° and cos 360°

c) tan 0°, tan 90°, tan 180°, tan 270° and tan 360°
11. 11
Find the exact value of:

a) sin $\frac{7\pi}{4}$

b) cos $\frac{\pi}{3}$
12. 12
Find the exact value of:

a) cos $\frac{3\pi}{4}$

b) tan $\frac{11\pi}{6}$
13. 13
Find the exact value of:

a) sin $\frac{11\pi}{6}$

b) cos $\frac{2\pi}{3}$
14. 14
Find the exact value for:

a) $sin 0, sin \frac{\pi}{2}, sin \pi, sin\frac{3\pi}{2}, sin 2\pi$

b) $cos 0, cos \frac{\pi}{2}, cos \pi, cos \frac{3\pi}{2}, cos 2\pi$

c) $tan 0, tan \frac{\pi}{2}, tan \pi, tan \frac{3\pi}{2}, tan 2\pi$

( trigonometry / trig )

$$e=mc^2$$