Solve Trigonometric Equations Using the Unit Circle
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- One way we can solve trigonometric functions is to plug in the equation into a calculator, but oftentimes, it's easier to use the unit circle! But before we dive into how to use…
By Anusha Rahman
- (Video) Solve Trig Equations with the Unit Circle by The How and Why of Mathematics In this video by The How and Why of Mathematics, you will learn about how to find exact solut…
By Anusha Rahman
- The Unit Circle for Trigonometric Equations We can use the unit circle to solve trigonometric equations. But first, let's review the unit circle. The unit circle can help us to …
By Anusha Rahman
Problems 21
- Find the largest solution to the equation sinx=cosx\sin x = \cos xsinx=cosx in the interval 0≤x<2π0 \le x < 2\pi0≤x<2π.
- Find all solutions on the interval 0≤θ<2π0\leq\theta<2\pi0≤θ<2π for 2sin(θ)=−1.\\2\sin(\theta)=-1.2sin(θ)=−1.
- Find all solutions on the interval 0≤θ<2π0\leq\theta<2\pi0≤θ<2π for 2sin(θ)=3.\\2\sin(\theta)=\sqrt3.2sin(θ)=3.
- Find all solutions on the interval 0≤θ<2π0\leq\theta<2\pi0≤θ<2π for 2cos(θ)=1.\\2\cos(\theta)=1.2cos(θ)=1.
- Find all solutions on the interval 0≤θ<2π0\leq\theta<2\pi0≤θ<2π for 2cos(θ)=−2.\\2\cos(\theta)=-\sqrt2.2cos(θ)=−2.
- Find all solutions for 2sin(π4x)=1.\\2\sin\left(\frac{\pi}4x\right)=1.2sin(4πx)=1.
- Find all solutions for 2sin(π3x)=2.\\2\sin(\frac{\pi}3x)=\sqrt2.2sin(3πx)=2.
- Find all solutions for 2cos(2t)=−3.\\2\cos(2t)=-\sqrt3.2cos(2t)=−3.
- Find all solutions for 2cos(3t)=−1.\\2\cos(3t)=-1.2cos(3t)=−1.
- Find all solutions for 3cos(π5x)=2.\\3\cos\left(\frac{\pi}5x\right)=2.3cos(5πx)=2.
- Find all solutions for 8cos(π2x)=6.\\8\cos\left(\frac{\pi}2x\right)=6.8cos(2πx)=6.
- Find all solutions for 7sin(3t)=−2.\\7\sin(3t)=-2.7sin(3t)=−2.
- Find all solutions for 4sin(4t)=1.\\4\sin(4t)=1.4sin(4t)=1.
- Find all solutions on the interval [0,2π)[0,2\pi)[0,2π) for −3sin(t)=15cos(t)sin(t).\\-3\sin(t)=15\cos(t)\sin(t).−3sin(t)=15cos(t)sin(t).
- Find all solutions on the interval [0,2π)[0,2\pi)[0,2π) for csc(2x)−9=0.\\\csc(2x)-9=0.csc(2x)−9=0.
- Find all solutions on the interval [0,π)[0,\pi)[0,π) for sec(2θ)=3.\\\sec(2\theta)=3.sec(2θ)=3.
- Find all solutions on the interval [0,2π)[0,2\pi)[0,2π) for sin2(x)=14.\\\sin^2(x)=\frac14.sin2(x)=41.
- Find all solutions on the interval [0,2π)[0,2\pi)[0,2π) for cos2(x)=12.\\\cos^2(x)=\frac12.cos2(x)=21.
- Find all solutions on the interval [0,2π)[0,2\pi)[0,2π) for sec2(x)=7.\\\sec^2(x)=7.sec2(x)=7.
- Find all solutions on the interval [0,2π)[0,2\pi)[0,2π) for csc2(t)=3.\\\csc^2(t)=3.csc2(t)=3.
- Find all solutions on the interval [0,2π)[0,2\pi)[0,2π) for 8cos2(θ)=3−2cos(θ).\\8\cos^2(\theta)=3-2\cos(\theta).8cos2(θ)=3−2cos(θ).