Solving Simple Trigonometric Equations

6 Activities

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

Solving Simple Trigonometric Equations

6 Activities

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.  

A) θ=5π12,7π12 ± 2nπ∈Z\theta=\dfrac{5\pi}{12},\dfrac{7\pi}{12}\ \pm{}\ 2n\pi{}\in\mathbb{Z}θ=125π​,127π​ ± 2nπ∈Z  

B) θ=5π6,7π6 ± nπ∈Z\theta=\dfrac{5\pi}{6},\dfrac{7\pi}{6}\ \pm{}\ n\pi{}\in\mathbb{Z}θ=65π​,67π​ ± nπ∈Z   

C) θ=5π12,7π12 ± nπ∈Z\theta=\dfrac{5\pi}{12},\dfrac{7\pi}{12}\ \pm{}\ n\pi{}\in\mathbb{Z}θ=125π​,127π​ ± nπ∈Z    

D) θ=5π6,7π6 ± 2nπ∈Z\theta=\dfrac{5\pi}{6},\dfrac{7\pi}{6}\ \pm{}\ 2n\pi{}\in\mathbb{Z}θ=65π​,67π​ ± 2nπ∈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 Ratios

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

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 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 Ratios

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

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 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 Equations

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