Trigonometry: Double-Angle Identities
Read this topicExplanations 5
- The double angle identities are really easy to derive. In this post, we'll show how to find formulas for sin2θ\sin{2\theta}sin2θ, cos2θ\cos{2\theta}cos2θ, and tan2θ\tan{2\the…
By Brandon Lin, Anusha Rahman
- The double angle formulas for the trig functions can often come in handy. I will present two proofs of them: a geometric one, and a purely algebraic one. First I will present a …
By Rajiv Movva
- The double-angle identities are identities that can be used to find the values of the trigonometric functions of double of an angle, given the values for the original angle. The…
By Sujay Kazi
- Trigonometry: Double-Angle Identities There are six negative angle identities you need to memorize! Negative angle identities Co-function identities Angle and sum differences id…
By Trisha, Anusha Rahman
- (Video) Double Angle Identities by Randy Anderson As we continue on our journey of trigonometry, we have learned about negative angle identities, co-function identities, and ang…
By Trisha, Anusha Rahman
Problems 31
- Let x=sin(A)x = \sin(A)x=sin(A). Using the general angle sum identities and the double angle identities, find sin(3A)\sin(3A)sin(3A) in terms of xxx.
- Find a value of xxx within 0≤x<π20 \le x < \frac\pi20≤x<2π where sin2x=cosx\sin 2x = \cos xsin2x=cosx. Express your answer in radians.
- Find the value of xxx in the interval (0,π)(0,\pi)(0,π) satisfying cos(2x)=cosx\cos(2x) = \cos xcos(2x)=cosx.
- Solve the equation sin2xsinx=3\frac{\sin 2x}{\sin x} = \sqrt3sinxsin2x=3 for solutions in the interval (0,π)(0,\pi)(0,π).
- What is the sum of all positive integer values of nnn that satisfy the equation cos(πn)cos(2πn)cos(4πn)cos(8πn)cos(16πn)=132?\cos \Bigl( \frac{\pi}{n} \Bigr) \cos \Bigl( \f…
- If sin(x)=18\sin(x)=\frac18sin(x)=81 and xxx is in quadrant I, then find an exact value for sin(2x)\sin(2x)sin(2x)
- If sin(x)=18\sin(x)=\frac18sin(x)=81 and xxx is in quadrant I, then find an exact value for cos(2x).\cos(2x).cos(2x).
- If sin(x)=18\sin(x)=\frac18sin(x)=81 and xxx is in quadrant I, then find an exact value for tan(2x)\tan(2x)tan(2x)
- If cos(x)=23\cos(x)=\frac23cos(x)=32 and xxx is in quadrant I, then find an exact value for sin(2x)\sin(2x)sin(2x)
- If cos(x)=23\cos(x)=\frac23cos(x)=32 and xxx is in quadrant I, then find an exact value for cos(2x).\cos(2x).cos(2x).
- If cos(x)=23\cos(x)=\frac23cos(x)=32 and xxx is in quadrant I, then find an exact value for tan(2x)\tan(2x)tan(2x)
- Simplify the expression cos2(28∘)−sin2(28∘)\\\cos^2(28^{\circ})-\sin^2(28^{\circ})cos2(28∘)−sin2(28∘)
- Simplify the expression 2cos2(37∘)−1\\2\cos^2(37^{\circ})-12cos2(37∘)−1
- Simplify the expression 1−2sin2(17∘)\\1-2\sin^2(17^{\circ})1−2sin2(17∘)
- Simplify the expression cos2(37∘)−sin2(37∘)\\\cos^2(37^{\circ})-\sin^2(37^{\circ})cos2(37∘)−sin2(37∘)
- Simplify the expression cos2(9x)−sin2(9x)\\\cos^2(9x)-\sin^2(9x)cos2(9x)−sin2(9x)
- Simplify the expression cos2(6x)−sin2(6x)\\\cos^2(6x)-\sin^2(6x)cos2(6x)−sin2(6x)
- Simplify the expression 4sin(8x)cos(8x).\\4\sin(8x)\cos(8x).4sin(8x)cos(8x).
- Simplify the expression 6sin(5x)cos(5x)\\6\sin(5x)\cos(5x)6sin(5x)cos(5x)
- Solve for all solutions on the interval [0,2π)[0,2\pi)[0,2π) 6sin(2t)+9sin(t)=0.\\6\sin(2t)+9\sin(t)=0.6sin(2t)+9sin(t)=0.
- Solve for all solutions on the interval [0,2π):[0,2\pi):[0,2π): 2sin(2t)+3cos(t)=0.\\2\sin(2t)+3\cos(t)=0.2sin(2t)+3cos(t)=0.
- Solve for all solutions on the interval [0,2π)[0,2\pi)[0,2π) 9cos(2θ)=9cos2(θ)−4\\9\cos(2\theta)=9\cos^2(\theta)-49cos(2θ)=9cos2(θ)−4
- Solve for all solutions on the interval [0,2π)[0,2\pi)[0,2π) 8cos(2θ)=8cos2(θ)−1\\8\cos(2\theta)=8\cos^2(\theta)-18cos(2θ)=8cos2(θ)−1
- Solve for all solutions on the interval [0,2π)[0,2\pi)[0,2π) cos(6x)−cos(3x)=0.\\\cos(6x)-\cos(3x)=0.cos(6x)−cos(3x)=0.
- Solve for all solutions on the interval [0,2π):[0,2\pi):[0,2π): cos(2t)=sin(t).\\\cos(2t)=\sin(t).cos(2t)=sin(t).
- Solve for all solutions on the interval [0,2π):[0,2\pi):[0,2π): sin(2t)=cos(t).\\\sin(2t)=\cos(t).sin(2t)=cos(t).
- 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 cos2(x)=12.\\\cos^2(x)=\frac12.cos2(x)=21.
- 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].
- 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).
- 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).