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Simplifying trig expressions with identities worksheets Grade 11

Simplify trig expressions by rewriting in sine and cosine.

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Free · Worked example · 21 problems · Answer key · US Letter

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How to do it

Rewrite in terms of sin and cos (tan = sin ÷ cos, sec = 1 ÷ cos, csc = 1 ÷ sin, cot = cos ÷ sin), or use sin² θ + cos² θ = 1.

1+ tan⁡2θ=(cos⁡2θ+ sin⁡2θ)÷ cos⁡2θ=sec⁡2θ1 +\ \tan ^{2} \theta = (\cos ^{2} \theta +\ \sin ^{2} \theta ) \div \ \cos ^{2} \theta = \sec ^{2} \theta write in terms of sin and cos, or use sin² θ + cos² θ = 1

Example problems

  1. sin⁡θ⋅ cot⁡θ=\sin \theta \cdot \ \cot \theta =
  2. 1− cos⁡2θ=1 -\ \cos ^{2} \theta =
  3. cos⁡θ⋅ tan⁡θ=\cos \theta \cdot \ \tan \theta =
  4. csc⁡θ⋅ tan⁡θ=\csc \theta \cdot \ \tan \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