Solving Quadratic Trigonometric Equations

5 Activities

Practice: Solving Quadratic Trigonometric Equations
Let 4sin⁡θcos⁡θ−1=04\sin\theta\cos\theta-1=04sinθcosθ−1=0. Find θ\thetaθ and the general solutions. 

A) π12, 5π12, ±2nπ, n∈I\dfrac{\pi}{12},~\dfrac{5\pi}{12},~\pm{}2n\pi,~n\in\mathbb{I}12π​, 125π​, ±2nπ, n∈I

B) π6, 5π6, ±2nπ, n∈I\dfrac{\pi}{6},~\dfrac{5\pi}{6},~\pm{}2n\pi,~n\in\mathbb{I}6π​, 65π​, ±2nπ, n∈I 

C) π6, 5π6, ±nπ, n∈I\dfrac{\pi}{6},~\dfrac{5\pi}{6},~\pm{}n\pi,~n\in\mathbb{I}6π​, 65π​, ±nπ, n∈I  

D) π12, 5π12, ±nπ, n∈I\dfrac{\pi}{12},~\dfrac{5\pi}{12},~\pm{}n\pi,~n\in\mathbb{I}12π​, 125π​, ±nπ, n∈I  

I don't know

Solving Quadratic Trigonometric Equations

Practice: Solving Quadratic Trigonometric Equations
Let 2tan⁡2θ=3tan⁡θ−12\tan^2\theta=3\tan\theta-12tan2θ=3tanθ−1. Find θ\thetaθ over the domain 0≤θ≤2π0\le\theta\le2\pi0≤θ≤2π.

Solving Quadratic Trigonometric Equations

Practice: Solving Quadratic Trigonometric Equations
Solve for θ\thetaθ over the domain 0≤θ≤2π0\leq{}\theta\leq{}2\pi0≤θ≤2π .
3sec⁡2θ−4=03\sec^2\theta-4=03sec2θ−4=0

Trigonometric Identities & Proofs

Solve for xxx over the domain 0≤x<2π0\leq{}x<2\pi0≤x<2π.
cos⁡2x=sin⁡x\cos{2x}=\sin{x}cos2x=sinx

Solving Quadratic Trigonometric Equations

Solve for θ\thetaθ over the domain −2π≤θ<2π-2\pi\leq\theta<2\pi−2π≤θ<2π.
2sin⁡2θ−sin⁡θ−32\sin^2\theta-\sin\theta-32sin2θ−sinθ−3

Solving Quadratic Trigonometric Equations

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Solving Quadratic Trigonometric Equations

Practice: Solving Quadratic Trigonometric Equations

More Solving Quadratic Trigonometric Equations Questions:

Solving Quadratic Trigonometric Equations

Solving Quadratic Trigonometric Equations

Trigonometric Identities & Proofs

Solving Quadratic Trigonometric Equations