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The unit circle worksheets Grade 11

Find exact trig values on the unit circle using reference angles and quadrant signs.

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Free · Worked example · 49 problems · Answer key · US Letter

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How to do it

Find the reference angle and its value, then the sign from the quadrant: sine is positive in I and II, cosine in I and IV, tangent in I and III.

tan⁡3π4=−1\tan \dfrac{3\pi }{4} = -1
reference angle π4, quadrant II: tan⁡ is negative there\text{reference angle }\dfrac{\pi }{4},\ \text{quadrant II: }\tan \ \text{is negative there}

Example problems

  1. sin⁡7π4=\sin \dfrac{7\pi }{4} =
  2. cos⁡7π4=\cos \dfrac{7\pi }{4} =
  3. sin⁡5π4=\sin \dfrac{5\pi }{4} =
  4. tan⁡135∘=\tan 135^{\circ} =

Trigonometry

  1. Right triangle trigonometry: sin, cos and tan
  2. Special right triangles and exact trig values
  3. Converting degrees and radians
  4. The unit circle
  5. Amplitude and period
  6. The Pythagorean identity
  7. Simplifying trig expressions with identities
  8. Solving trigonometric equations
  9. The law of cosines
  10. The law of sines