Trigonometric identities and solving trigonometric equations
Simplify expressions using the Pythagorean/double-angle/quotient identities, and solve trig equations exactly on [0, 2pi). Unlimited questions, five difficulty levels, and a full worked solution every time, included free with weekly lessons.
Try one
Solve the equation for x on the interval [0, 2pi).
cos(x) = 12
- x = π/6
- x = 5pi/6, 7pi/6
- x = π/6, 7pi/6
- x = π/6, 11pi/6
Answer: x = pi/6, 11pi/6
See one solved, step by step
Solve the equation for x on the interval [0, 2pi).
2cos(x) - √(3) = 0
- x = π/3
- x = 2pi/3, 4pi/3
- x = π/3, 2pi/3
- x = π/3, 5pi/3
📘 Worked solution
12cos(x) - √(3) = 0Start with the equation.
2cos(x) = √(3)/2Isolate cos(x) by moving the constant and dividing by 2.
3Reference angle: π/3. cos is positive in quadrants I and IV.The reference angle comes from the special triangles; the sign picks the quadrants.
4x = π/3, 5pi/3Place the reference angle in each of the two matching quadrants.
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