Solving Simple Trigonometric Ratios

Solving Simple Trigonometric Equations

6 Activities

Wize High School Algebra II Textbook (Common Core) > Trigonometric Ratios (Radians)

Solving Simple Trigonometric Equations

6 Activities

Solve for θ\thetaθ over the interval (−∞,∞)(-\infin,\infin)(−∞,∞):
4cos⁡3θ=24\cos3\theta=24cos3θ=2

A) θ=π3, 5π3±2nπ, n∈Z+\theta=\dfrac{\pi}{3},~\dfrac{5\pi}{3}\pm2n\pi,~n\in\mathbb{Z^{+}}θ=3π​, 35π​±2nπ, n∈Z+ 

B) θ=π6, 5π6±23nπ, n∈Z+\theta=\dfrac{\pi}{6},~\dfrac{5\pi}{6}\pm\dfrac{2}{3}n\pi,~n\in\mathbb{Z^{+}}θ=6π​, 65π​±32​nπ, n∈Z+ 

C) θ=π9, 5π9±2nπ, n∈Z+\theta=\dfrac{\pi}{9},~\dfrac{5\pi}{9}\pm2n\pi,~n\in\mathbb{Z^{+}}θ=9π​, 95π​±2nπ, n∈Z+ 

D) θ=π9, 5π9±23nπ, n∈Z+\theta=\dfrac{\pi}{9},~\dfrac{5\pi}{9}\pm\dfrac{2}{3}n\pi,~n\in\mathbb{Z^{+}}θ=9π​, 95π​±32​nπ, n∈Z+ 

I don't know

Solving Trigonometric Equations

Find aaa over the domain 0≤a<2π0\leq{}a<2\pi0≤a<2π
cot⁡a2=1\cot\dfrac{a}{2}=1cot2a​=1

Solving Simple Trigonometric Equations

Solve for θ\thetaθ over the domain 0≤θ<2π0\leq{}\theta<2\pi0≤θ<2π
2sin⁡θ=−22\sin\theta=-\sqrt{2}2sinθ=−2​

Solving Simple Trigonometric Equations

Practice: Solving Simple Trigonometric Equations
Let tan⁡2θ=1\tan{2\theta}=1tan2θ=1. Solve for θ\thetaθ, providing the general solution. 

Solving Simple Trigonometric Equations

Practice: Solving Simple Trigonometric Equations
Let cos⁡2θ=−32\cos{2\theta}=-\dfrac{\sqrt{3}}{2}cos2θ=−23​​. Solve for θ\thetaθ, providing the general solution.  

Solving Simple Trigonometric Equations

Practice: Solving Simple Trigonometric Equations
Let 32sec⁡θ−2sec⁡θ=43\sqrt{2}\sec{\theta}-\sqrt{2}\sec{\theta}=432​secθ−2​secθ=4. Solve for θ \theta~θ  over the domain 0≤θ<2π0\leq{\theta}<2\pi0≤θ<2π.

Solving Simple Trigonometric Equations

Practice: Solving Simple Trigonometric Equations
Let 4sin⁡θ−2sin⁡θ=14\sin\theta-2\sin\theta=14sinθ−2sinθ=1. Solve for θ \theta~θ  over the domain 0≤θ<2π0\leq{\theta}<2\pi0≤θ<2π.

Solving Simple Trigonometric Equations

Practice: Solving Simple Trigonometric Equations
Solve cos⁡θ=12\cos{\theta}=\dfrac{1}{\sqrt{2}}cosθ=2​1​ over the domain 0≤θ<2π0\leq{}\theta<2\pi0≤θ<2π.

Solving Simple Trigonometric Equations

Practice: Solving Simple Trigonometric Equations
Solve sin⁡θ=−32\sin{\theta}=-\dfrac{\sqrt{3}}{2}sinθ=−23​​ over the domain 0≤θ<2π0\leq{}\theta<2\pi0≤θ<2π.

Solving Trigonometric Equations

Find aaa over the domain 0≤a<2π0\leq{}a<2\pi0≤a<2π
cot⁡a2=1\cot\dfrac{a}{2}=1cot2a​=1

Solving Simple Trigonometric Equations

Solve for θ\thetaθ over the domain 0≤θ<2π0\leq{}\theta<2\pi0≤θ<2π
2sin⁡θ=−22\sin\theta=-\sqrt{2}2sinθ=−2​

Solving Simple Trigonometric Equations

Practice: Solving Simple Trigonometric Equations
Let tan⁡2θ=1\tan{2\theta}=1tan2θ=1. Solve for θ\thetaθ, providing the general solution. 

Solving Simple Trigonometric Equations

Practice: Solving Simple Trigonometric Equations
Let cos⁡2θ=−32\cos{2\theta}=-\dfrac{\sqrt{3}}{2}cos2θ=−23​​. Solve for θ\thetaθ, providing the general solution.  

Solving Simple Trigonometric Equations

Practice: Solving Simple Trigonometric Equations
Let 32sec⁡θ−2sec⁡θ=43\sqrt{2}\sec{\theta}-\sqrt{2}\sec{\theta}=432​secθ−2​secθ=4. Solve for θ \theta~θ  over the domain 0≤θ<2π0\leq{\theta}<2\pi0≤θ<2π.

Solving Simple Trigonometric Equations

Practice: Solving Simple Trigonometric Equations
Let 4sin⁡θ−2sin⁡θ=14\sin\theta-2\sin\theta=14sinθ−2sinθ=1. Solve for θ \theta~θ  over the domain 0≤θ<2π0\leq{\theta}<2\pi0≤θ<2π.

Solving Simple Trigonometric Equations

Practice: Solving Simple Trigonometric Equations
Solve cos⁡θ=12\cos{\theta}=\dfrac{1}{\sqrt{2}}cosθ=2​1​ over the domain 0≤θ<2π0\leq{}\theta<2\pi0≤θ<2π.

Solving Simple Trigonometric Equations

Practice: Solving Simple Trigonometric Equations
Solve sin⁡θ=−32\sin{\theta}=-\dfrac{\sqrt{3}}{2}sinθ=−23​​ over the domain 0≤θ<2π0\leq{}\theta<2\pi0≤θ<2π.

Solving Simple Trigonometric Ratios

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