What is the general solution for 2sin(5x)+sqrt(3)=0,0<= x<= 2pi ?

The general solution for 2sin(5x)+sqrt(3)=0,0<= x<= 2pi is

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2sin(5x)+sqrt(3)=0,0<= x<= 2pi

2 sin (5 x) + 3 = 0, 0 \leq x \leq 2 π

x = \frac{4 π}{15}, x = \frac{π}{3}, x = \frac{2 π}{3}, x = \frac{11 π}{15}, x = \frac{16 π}{15}, x = \frac{17 π}{15}, x = \frac{22 π}{15}, x = \frac{23 π}{15}, x = \frac{28 π}{15}, x = \frac{29 π}{15}

Solution steps

2 sin (5 x) + 3 = 0, 0 \leq x \leq 2 π

Move

3

to the right side

2 sin (5 x) = - 3

Divide both sides by

2

sin (5 x) = - \frac{3}{2}

General solutions for

sin (5 x) = - \frac{3}{2}

5 x = \frac{4 π}{3} + 2 πn, 5 x = \frac{5 π}{3} + 2 πn

Solve

5 x = \frac{4 π}{3} + 2 πn : x = \frac{4 π}{15} + \frac{2 πn}{5}

Solve

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

x = \frac{4 π}{15} + \frac{2 πn}{5}, x = \frac{π}{3} + \frac{2 πn}{5}

Solutions for the range

0 \leq x \leq 2 π

x = \frac{4 π}{15}, x = \frac{π}{3}, x = \frac{2 π}{3}, x = \frac{11 π}{15}, x = \frac{16 π}{15}, x = \frac{17 π}{15}, x = \frac{22 π}{15}, x = \frac{23 π}{15}, x = \frac{28 π}{15}, x = \frac{29 π}{15}

sin (2 θ) = - \frac{24}{25}

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

What is the general solution for 2sin(5x)+sqrt(3)=0,0<= x<= 2pi ?
The general solution for 2sin(5x)+sqrt(3)=0,0<= x<= 2pi is