What is the general solution for cos(θ/3)=sin(θ) ?

The general solution for cos(θ/3)=sin(θ) is θ=(3pi+12pin)/8 ,θ=(3pi+12pin)/4

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cos(θ/3)=sin(θ)

cos (\frac{θ}{3}) = sin (θ)

θ = \frac{3 π + 12 πn}{8}, θ = \frac{3 π + 12 πn}{4}

Solution steps

cos (\frac{θ}{3}) = sin (θ)

Rewrite using trig identities

cos (\frac{θ}{3}) = sin (\frac{π}{2} - \frac{θ}{3})

Apply trig inverse properties

θ = \frac{π}{2} - \frac{θ}{3} + 2 πn, θ = π - (\frac{π}{2} - \frac{θ}{3}) + 2 πn

θ = \frac{π}{2} - \frac{θ}{3} + 2 πn : θ = \frac{3 π + 12 πn}{8}

θ = π - (\frac{π}{2} - \frac{θ}{3}) + 2 πn : θ = \frac{3 π + 12 πn}{4}

θ = \frac{3 π + 12 πn}{8}, θ = \frac{3 π + 12 πn}{4}

sin (x) - cos (x) = \frac{1}{5}

tan (θ) = \frac{- 2}{3}

cos (θ) tan^{2} (θ) = 3 cos (θ)

cos (θ) = 0.56

cos (θ) = 0.17

What is the general solution for cos(θ/3)=sin(θ) ?
The general solution for cos(θ/3)=sin(θ) is θ=(3pi+12pin)/8 ,θ=(3pi+12pin)/4