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 )

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