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The Pythagorean identity worksheets Grade 11

Use sin² θ + cos² θ = 1 to find a missing trig value and its sign.

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How to do it

sin² θ + cos² θ = 1. Find the missing value, then choose its sign from the quadrant.

sin⁡θ=−1237,θ in quadrant IV: tan⁡θ=−1235\sin \theta = -\dfrac{12}{37}, \theta \ \text{in quadrant IV: }\tan \theta = -\dfrac{12}{35}
cos⁡2θ=1−(−1237)2=12251369\cos ^{2} \theta = 1 - (-\dfrac{12}{37})^{2} = \dfrac{1225}{1369}sin² θ + cos² θ = 1
cos⁡θ=3537\cos \theta = \dfrac{35}{37}cos is positive in quadrant IV
tan⁡θ= sin⁡θ÷ cos⁡θ=−1235\tan \theta =\ \sin \theta \div \ \cos \theta = -\dfrac{12}{35}

Example problems

  1. cos⁡θ=4041,θ in quadrant I: tan⁡θ=\cos \theta = \dfrac{40}{41}, \theta \ \text{in quadrant I: }\tan \theta =
  2. sin⁡θ=−725,θ in quadrant IV: cos⁡θ=\sin \theta = -\dfrac{7}{25}, \theta \ \text{in quadrant IV: }\cos \theta =
  3. cos⁡θ=1213,θ in quadrant IV: sin⁡θ=\cos \theta = \dfrac{12}{13}, \theta \ \text{in quadrant IV: }\sin \theta =
  4. sin⁡θ=−513,θ in quadrant IV: cos⁡θ=\sin \theta = -\dfrac{5}{13}, \theta \ \text{in quadrant IV: }\cos \theta =

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