What is the general solution for sin(θ)=cos(37) ?

The general solution for sin(θ)=cos(37) is θ=360n+53,θ=180-53+360n

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sin(θ)=cos(37)

sin (θ) = cos (3 7^{\circ})

θ = 36 0^{\circ} n + 5 3^{\circ}, θ = 18 0^{\circ} - 5 3^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = cos (3 7^{\circ})

Rewrite using trig identities

sin (θ) = sin (9 0^{\circ} - 3 7^{\circ})

Apply trig inverse properties

θ = 9 0^{\circ} - 3 7^{\circ} + 36 0^{\circ} n, θ = 18 0^{\circ} - (9 0^{\circ} - 3 7^{\circ}) + 36 0^{\circ} n

θ = 9 0^{\circ} - 3 7^{\circ} + 36 0^{\circ} n : θ = 36 0^{\circ} n + 5 3^{\circ}

θ = 18 0^{\circ} - (9 0^{\circ} - 3 7^{\circ}) + 36 0^{\circ} n : θ = 18 0^{\circ} - 5 3^{\circ} + 36 0^{\circ} n

θ = 36 0^{\circ} n + 5 3^{\circ}, θ = 18 0^{\circ} - 5 3^{\circ} + 36 0^{\circ} n

cot (x) - cot (x) csc (x) = 0

3 sin^{2} (x) - 3 sin (x) + cos^{2} (x) = 0

12 cos^{2} (x) - 7 cos (x) + 1 = 0

tan (\frac{x}{2}) tan (x) = - 3

sin (- x) = - \frac{1}{3}, tan (x) = - \frac{2}{4}

What is the general solution for sin(θ)=cos(37) ?
The general solution for sin(θ)=cos(37) is θ=360n+53,θ=180-53+360n