What is the general solution for 52800=((1500)^2sin(x))/(32.2) ?

The general solution for 52800=((1500)^2sin(x))/(32.2) is x=0.85661…+2pin,x=pi-0.85661…+2pin

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52800=((1500)^2sin(x))/(32.2)

52800 = \frac{( 1500 ) ^{2} sin ( x )}{32.2}

x = 0.85661 \dots + 2 πn, x = π - 0.85661 \dots + 2 πn

Degrees

x = 49.08015 \dots^{\circ} + 36 0^{\circ} n, x = 130.91984 \dots^{\circ} + 36 0^{\circ} n

Solution steps

52800 = \frac{( 1500 ) ^{2} sin ( x )}{32.2}

Switch sides

\frac{150 0 ^{2} sin ( x )}{32.2} = 52800

Multiply both sides by

32.2

\frac{150 0 ^{2} sin ( x )}{32.2} = 52800

Multiply both sides by

32.2

\frac{32.2 \cdot 150 0 ^{2} sin ( x )}{32.2} = 52800 \cdot 32.2

Simplify

2250000 sin (x) = 1700160

2250000 sin (x) = 1700160

Divide both sides by

2250000

2250000 sin (x) = 1700160

Divide both sides by

2250000

\frac{2250000 sin ( x )}{2250000} = \frac{1700160}{2250000}

Simplify

sin (x) = \frac{7084}{9375}

sin (x) = \frac{7084}{9375}

Apply trig inverse properties

sin (x) = \frac{7084}{9375}

General solutions for

sin (x) = \frac{7084}{9375}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

x = arcsin (\frac{7084}{9375}) + 2 πn, x = π - arcsin (\frac{7084}{9375}) + 2 πn

x = arcsin (\frac{7084}{9375}) + 2 πn, x = π - arcsin (\frac{7084}{9375}) + 2 πn

Show solutions in decimal form

x = 0.85661 \dots + 2 πn, x = π - 0.85661 \dots + 2 πn

7 cos (3 x) = 2, 0 \leq x < 2 π

6 cos (2 x) = 3

arctan (\frac{x}{42}) = 57

3 tan^{2} (x) = 19

3.6 = 0.116 cos (4.17 x)

What is the general solution for 52800=((1500)^2sin(x))/(32.2) ?
The general solution for 52800=((1500)^2sin(x))/(32.2) is x=0.85661…+2pin,x=pi-0.85661…+2pin