What is the general solution for sin(5x)=-1 ?

The general solution for sin(5x)=-1 is x=(3pi}{10}+\frac{2pin)/5

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sin(5x)=-1

sin (5 x) = - 1

x = \frac{3 π}{10} + \frac{2 πn}{5}

Solution steps

sin (5 x) = - 1

General solutions for

sin (5 x) = - 1

5 x = \frac{3 π}{2} + 2 πn

Solve

5 x = \frac{3 π}{2} + 2 πn : x = \frac{3 π}{10} + \frac{2 πn}{5}

x = \frac{3 π}{10} + \frac{2 πn}{5}

tan^{2} (x) + 3 sec (x) = - 3

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

sin (2 x) = - 5 cos (2 x), 0 \leq x \leq 2 π

2 cos^{2} (x) + 9 cos (x) - 5 = 0

cos (θ) = - \frac{3}{4}

What is the general solution for sin(5x)=-1 ?
The general solution for sin(5x)=-1 is x=(3pi}{10}+\frac{2pin)/5