What is the general solution for 3cos(2θ)=3sin(θ) ?

The general solution for 3cos(2θ)=3sin(θ) is θ=(3pi)/2+2pin,θ= pi/6+2pin,θ=(5pi)/6+2pin

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3cos(2θ)=3sin(θ)

3 cos (2 θ) = 3 sin (θ)

θ = \frac{3 π}{2} + 2 πn, θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

Solution steps

3 cos (2 θ) = 3 sin (θ)

Subtract

3 sin (θ)

from both sides

3 cos (2 θ) - 3 sin (θ) = 0

Rewrite using trig identities

(1 - 2 sin^{2} (θ)) \cdot 3 - 3 sin (θ) = 0

Solve by substitution

sin (θ) = - 1, sin (θ) = \frac{1}{2}

sin (θ) = - 1 : θ = \frac{3 π}{2} + 2 πn

sin (θ) = \frac{1}{2} : θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

Combine all the solutions

θ = \frac{3 π}{2} + 2 πn, θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

cos^{2} (x) = 1 - cos^{2} (x), [36 0^{\circ}]

tan (t) = - \frac{12}{5}, \frac{3 π}{2} < t < 2 π, sin (t)

tan (6. 5^{2} - a) = 8

- 10 cos (θ) = - 2 - 6 cos (θ)

sin (a) = (\frac{( 8 )}{( 153 )})

What is the general solution for 3cos(2θ)=3sin(θ) ?
The general solution for 3cos(2θ)=3sin(θ) is θ=(3pi)/2+2pin,θ= pi/6+2pin,θ=(5pi)/6+2pin