What is the general solution for sin(2θ)=-24/25 ?

The general solution for sin(2θ)=-24/25 is θ=-(1.28700…)/2+pin,θ= pi/2+(1.28700…)/2+pin

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sin(2θ)=-24/25

sin (2 θ) = - \frac{24}{25}

θ = - \frac{1.28700 \dots}{2} + πn, θ = \frac{π}{2} + \frac{1.28700 \dots}{2} + πn

Solution steps

sin (2 θ) = - \frac{24}{25}

Apply trig inverse properties

2 θ = arcsin (- \frac{24}{25}) + 2 πn, 2 θ = π + arcsin (\frac{24}{25}) + 2 πn

Solve

2 θ = arcsin (- \frac{24}{25}) + 2 πn : θ = - \frac{arcsin ( \frac{24}{25} )}{2} + πn

Solve

2 θ = π + arcsin (\frac{24}{25}) + 2 πn : θ = \frac{π}{2} + \frac{arcsin ( \frac{24}{25} )}{2} + πn

θ = - \frac{arcsin ( \frac{24}{25} )}{2} + πn, θ = \frac{π}{2} + \frac{arcsin ( \frac{24}{25} )}{2} + πn

Show solutions in decimal form

θ = - \frac{1.28700 \dots}{2} + πn, θ = \frac{π}{2} + \frac{1.28700 \dots}{2} + πn

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

- 4 cos (x) = - sin^{2} (x) + 4, 0 \leq x \leq 2 π

0 = cos^{2} (\frac{π}{12} t)

sec^{2} (x) + 2 sec (x) + 4 = 0

cos (A) = 0.7865

What is the general solution for sin(2θ)=-24/25 ?
The general solution for sin(2θ)=-24/25 is θ=-(1.28700…)/2+pin,θ= pi/2+(1.28700…)/2+pin