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Solving trigonometric equations worksheets Grade 11

Solve trig equations for every angle from 0 to 2π.

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Free · Worked example · 15 problems · Answer key · US Letter

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How to do it

Get the trig function alone, find the reference angle, and list every angle from 0 to 2π in the quadrants with the right sign.

2 sin⁡x−1=0,0≤x<2π:x=π6 or x=5π62\ \sin x - 1 = 0,\quad 0 \le x < 2\pi :\quad x = \dfrac{\pi }{6}\ \text{or }x = \dfrac{5\pi }{6}
sin⁡x=12\sin x = \dfrac{1}{2}get sin x alone
x=π6 or x=5π6x = \dfrac{\pi }{6}\ \text{or }x = \dfrac{5\pi }{6}every angle from 0 to 2π with that value

Example problems

  1. 2 cos⁡x−1=0,0≤x<2π:2\ \cos x - 1 = 0,\quad 0 \le x < 2\pi :\quad
  2. 2 cos⁡x−2=0,0≤x<2π:2\ \cos x - \sqrt{2} = 0,\quad 0 \le x < 2\pi :\quad
  3. tan⁡x−3=0,0≤x<2π:\tan x - \sqrt{3} = 0,\quad 0 \le x < 2\pi :\quad
  4. 2 sin⁡x+2=0,0≤x<2π:2\ \sin x + \sqrt{2} = 0,\quad 0 \le x < 2\pi :\quad

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