Solve Trigonometric Equations Using Identities and Factoring
Read this topicExplanations 4
- Our goal is to solve trigonometric equations that have one variable. In most trigonometric equations, the variable appears inside a trigonometric function, such as sine, cosine,…
By Joshua Siktar, Anusha Rahman
- So far, we have learned many trigonometric identities. We have also learned several ways to solve equations, especially linear and quadratic equations. Now it’s time to combine …
By Joshua Siktar, Victor Wang, Anusha Rahman
- (Video) Solving Trigonometric Equations By Factoring & By Using Double Angle Identities by The Organic Chemistry Tutor In this video by [The Organic Chemistry Tutor](Solving Tri…
By Anusha Rahman
- Solve Trigonometric Equations with Identities and Factoring When we solve trig equations, we often use special math rules called identities. These rules help you rewrite the equ…
By Anusha Rahman
Problems 52
- Solve the following equation for xxx in the interval [−π2,π2]:\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]:[−2π,2π]: sinx+sin2x=cos2x.\sin x + \sin^2 x = \cos^2 x.sinx+sin2x=…
- 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 on the interval [0,2π)[0,2\pi)[0,2π) for 10sin(x)cos(x)=6cos(x).\\10\sin(x)\cos(x)=6\cos(x).10sin(x)cos(x)=6cos(x).
- 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 sec(x)sin(x)−2sin(x)=0.\\\sec(x)\sin(x)-2\sin(x)=0.sec(x)sin(x)−2sin(x)=0.
- Find all solutions on the interval [0,2π)[0,2\pi)[0,2π) for tan(x)sin(x)−sin(x)=0.\\\tan(x)\sin(x)-\sin(x)=0.tan(x)sin(x)−sin(x)=0.
- 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 2sin2(w)+3sin(w)+1=0.\\2\sin^2(w)+3\sin(w)+1=0.2sin2(w)+3sin(w)+1=0.
- Find all solutions on the interval [0,2π)[0,2\pi)[0,2π) for 8sin2(x)+6sin(x)+1=0.\\8\sin^2(x)+6\sin(x)+1=0.8sin2(x)+6sin(x)+1=0.
- Find all solutions on the interval [0,2π)[0,2\pi)[0,2π) for 2cos2(t)+cos(t)=1.\\2\cos^2(t)+\cos(t)=1.2cos2(t)+cos(t)=1.
- 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).
- Find all solutions on the interval [0,2π)[0,2\pi)[0,2π) for 4cos2(x)−4=15cos(x).\\4\cos^2(x)-4=15\cos(x).4cos2(x)−4=15cos(x).
- Find all solutions on the interval [0,2π)[0,2\pi)[0,2π) for 9sin(w)−2=4sin2(w).\\9\sin(w)-2=4\sin^2(w).9sin(w)−2=4sin2(w).
- Find all solutions on the interval [0,2π)[0,2\pi)[0,2π) for 12sin2(t)+cos(t)−6=0.\\12\sin^2(t)+\cos(t)-6=0.12sin2(t)+cos(t)−6=0.
- Find all solutions on the interval [0,2π)[0,2\pi)[0,2π) for 6cos2(x)+7sin(x)−8=0.\\6\cos^2(x)+7\sin(x)-8=0.6cos2(x)+7sin(x)−8=0.
- Find all solutions on the interval [0,2π)[0,2\pi)[0,2π) for cos2(x)=−6sin(x).\\\cos^2(x)=-6\sin(x).cos2(x)=−6sin(x).
- Find all possible values of cos(t)\cos(t)cos(t) if sin2(t)=cos(t).\\\sin^2(t)=\cos(t).sin2(t)=cos(t).
- Find all solutions on the interval [0,2π)[0,2\pi)[0,2π) for tan3(x)=3tan(x).\\\tan^3(x)=3\tan(x).tan3(x)=3tan(x).
- Find all solutions on the interval [0,2π)[0,2\pi)[0,2π) for cos3(t)=−cos(t).\\\cos^3(t)=-\cos(t).cos3(t)=−cos(t).
- Find all solutions on the interval [0,2π)[0,2\pi)[0,2π) for tan5(x)=tan(x).\\\tan^5(x)=\tan(x).tan5(x)=tan(x).
- Find all solutions on the interval [0,2π)[0,2\pi)[0,2π) for tan5(x)−9tan(x)=0.\\\tan^5(x)-9\tan(x)=0.tan5(x)−9tan(x)=0.
- Find all solutions on the interval [0,2π)[0,2\pi)[0,2π) for 4sin(x)cos(x)+2sin(x)−2cos(x)−1=0.\\4\sin(x)\cos(x)+2\sin(x)-2\cos(x)-1=0.4sin(x)cos(x)+2sin(x)−2cos(x)−1=0.
- Find all solutions on the interval [0,2π)[0,2\pi)[0,2π) for 2sin(x)cos(x)−sin(x)+2cos(x)−1=0.\\2\sin(x)\cos(x)-\sin(x)+2\cos(x)-1=0.2sin(x)cos(x)−sin(x)+2cos(x)−1=0.
- Find all solutions on the interval [0,2π)[0,2\pi)[0,2π) for tan(x)−3sin(x)=0.\\\tan(x)-3\sin(x)=0.tan(x)−3sin(x)=0.
- Find all solutions on the interval [0,2π)[0,2\pi)[0,2π) for 3cos(x)=cot(x).\\3\cos(x)=\cot(x).3cos(x)=cot(x).
- Find all solutions on the interval [0,2π)[0,2\pi)[0,2π) for 2tan2(t)=3sec(t).\\2\tan^2(t)=3\sec(t).2tan2(t)=3sec(t).
- Find all solutions on the interval [0,2π)[0,2\pi)[0,2π) for 1−2tan(w)=tan2(w).\\1-2\tan(w)=\tan^2(w).1−2tan(w)=tan2(w).
- Find all possible values of sin(x)\sin(x)sin(x) if 4cos2x=2sin2x−1.4\cos^2x=2\sin^2x-1.4cos2x=2sin2x−1.
- Solve cos3(α)−sin3(α)=0\cos^3(\alpha) - \sin^3(\alpha) = 0cos3(α)−sin3(α)=0 on the interval [0,π].[0, \pi].[0,π].
- Solve the equation sin2(x)+3cos2(x)=0\sin^2(x) + 3\cos^2(x) = 0sin2(x)+3cos2(x)=0 in the domain [0,2π].[0, 2\pi].[0,2π].
- There is one solution to the equation sin5(x)+2sin3(x)cos2(x)+sin(x)cos4(x)=1\sin^5(x) + 2\sin^3(x)\cos^2(x) + \sin(x)\cos^4(x) = 1sin5(x)+2sin3(x)cos2(x)+sin(x)cos4(x)=1 i…
- Solve the following equation in x∈[0,2π]:x \in [0, 2\pi]:x∈[0,2π]: sin2(x)+cos2(x)+tan2(x)=csc2(x).\sin^2(x) + \cos^2(x) + \tan^2(x) = \csc^2(x).sin2(x)+cos2(x)+tan2(x)=csc2…
- If xxx is a real number for which cos(2x)=710,\cos(2x) = \frac{7}{10},cos(2x)=107, find the value of sin2(x).\sin^2(x).sin2(x).
- Solve the equation cos2(y)−9cos(y)+14=0\cos^2(y) - 9\cos(y) + 14 = 0cos2(y)−9cos(y)+14=0 for y∈[0,2π).y \in [0, 2\pi).y∈[0,2π).
- Find all possible values of sin(x)\sin(x)sin(x) if xxx is a real number for which tan(2x)cos(x)=3.\frac{\tan(2x)}{\cos(x)} = 3.cos(x)tan(2x)=3.
- Find all possible values of sin(x)\sin(x)sin(x) if xxx is a real number for which tan(2x)cos(x)=−2.\frac{\tan(2x)}{\cos(x)} = -2.cos(x)tan(2x)=−2.
- If xxx is a real number such that tan(2x)cos(x)=4,\frac{\tan(2x)}{\cos(x)} = 4,cos(x)tan(2x)=4, find the possible value(s) of sin(x).\sin(x).sin(x).
- Identify the solution(s) to the equation tan2(x)−sin2(x)−sin2(x)tan2(x)=0.\tan^2(x) - \sin^2(x) - \sin^2(x)\tan^2(x) = 0.tan2(x)−sin2(x)−sin2(x)tan2(x)=0.
- Find all solutions to sin2019(x)+2019sin2021(x)=0\sin^{2019}(x) + 2019\sin^{2021}(x) = 0sin2019(x)+2019sin2021(x)=0 in the interval [0,2π).[0, 2\pi).[0,2π).
- Find all solutions (x,y)∈[0,2π)×[0,2π)(x, y)\in [0,2\pi)\times[0,2\pi)(x,y)∈[0,2π)×[0,2π) to the system of equations cos(x)cos(y)−cos(x)+cos(y)−1=0\cos(x)\cos(y) - \cos(x) +…
- Which of the following are solutions to csc2(x)+2csc(x)+7=0?\csc^2(x) + 2\csc(x) + 7 = 0?csc2(x)+2csc(x)+7=0?
- Find all solutions to sec2(x)+2sec(x)+7=0.\sec^2(x) + 2\sec(x) + 7 = 0.sec2(x)+2sec(x)+7=0.
- Which of the following are solutions to cos2(x)−21cos(x)=−110?\cos^2(x) - 21\cos(x) = -110?cos2(x)−21cos(x)=−110?
- Which of the following are solutions to sin(8x)−sin(4x)=0\sin(8x) - \sin(4x) = 0sin(8x)−sin(4x)=0 in the interval [0,π]?[0, \pi]?[0,π]?
- Which of the following are solutions to 1=2sin(x)cos(x)tan(2x)1−2sin2(x)1 = \frac{2\sin(x)\cos(x)\tan(2x)}{1 - 2\sin^2(x)}1=1−2sin2(x)2sin(x)cos(x)tan(2x) in the interval […
- If xxx is a real number such that cos(2x)=710,\cos(2x) = \frac{7}{10},cos(2x)=107, find the value of cos2(x).\cos^2(x).cos2(x).