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Popular >

cos(θ)-cos(3θ)=0

Solution

cos (θ) - cos (3 θ) = 0

Solution

θ = πn, θ = \frac{π}{2} + πn

+1

Solution steps

cos (θ) - cos (3 θ) = 0

Rewrite using trig identities

2 sin (2 θ) sin (θ) = 0

Solving each part separately

sin (2 θ) = 0 or sin (θ) = 0

sin (2 θ) = 0 : θ = πn, θ = \frac{π}{2} + πn

sin (θ) = 0 : θ = 2 πn, θ = π + 2 πn

Combine all the solutions

θ = πn, θ = \frac{π}{2} + πn, θ = 2 πn, θ = π + 2 πn

Merge Overlapping Intervals

θ = πn, θ = \frac{π}{2} + πn

Popular Examples

-tan(2θ)+2sin(θ)=0,0<= θ<2pi

- tan (2 θ) + 2 sin (θ) = 0, 0 \leq θ < 2 π

cos(x)=(2tan(x))/(1+tan^2(x))

cos (x) = \frac{2 tan ( x )}{1 + tan ^{2} ( x )}

(1+cos(4x))sin(2x)=cos^2(2x)

(1 + cos (4 x)) sin (2 x) = cos^{2} (2 x)

cos(2x)-cos(6x)-sin(4x)=0

cos (2 x) - cos (6 x) - sin (4 x) = 0

cot (θ) = \frac{15}{8}

Frequently Asked Questions (FAQ)

What is the general solution for cos(θ)-cos(3θ)=0 ?
The general solution for cos(θ)-cos(3θ)=0 is θ=pin,θ= pi/2+pin