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a⋅(trig function)2+b⋅(trig function)+c=0a \cdot (\text{trig function})^2 + b \cdot (\text{trig function}) + c = 0a⋅(trig function)2+b⋅(trig function)+c=0
Use substitution, rearrangement, and factoring techniques.
u=−b±b2−4ac2au = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}u=2a−b±b2−4ac
Replace uuu with the original trigonometric function.
Typically 0°0°0° to 360°360°360° or 000 to 2π2\pi2π radians.
θ=210°\theta = 210°θ=210° or θ=330°\theta = 330°θ=330°.
cos(θ)\cos(\theta)cos(θ) must be between −1-1−1 and 111.
θ=90°+180°k\theta = 90° + 180°kθ=90°+180°k, where kkk is any integer.
θ=60°,120°,240°,300°\theta = 60°, 120°, 240°, 300°θ=60°,120°,240°,300°.
Use quadratic formula and check valid cos values.
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