What is the general solution for sin(2x)= 21/25 ?

The general solution for sin(2x)= 21/25 is x=(0.99728…)/2+pin,x= pi/2-(0.99728…)/2+pin

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sin(2x)= 21/25

sin (2 x) = \frac{21}{25}

x = \frac{0.99728 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.99728 \dots}{2} + πn

Degrees

x = 28.57005 \dots^{\circ} + 18 0^{\circ} n, x = 61.42994 \dots^{\circ} + 18 0^{\circ} n

Solution steps

sin (2 x) = \frac{21}{25}

Apply trig inverse properties

sin (2 x) = \frac{21}{25}

General solutions for

sin (2 x) = \frac{21}{25}

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

2 x = arcsin (\frac{21}{25}) + 2 πn, 2 x = π - arcsin (\frac{21}{25}) + 2 πn

2 x = arcsin (\frac{21}{25}) + 2 πn, 2 x = π - arcsin (\frac{21}{25}) + 2 πn

Solve

2 x = arcsin (\frac{21}{25}) + 2 πn : x = \frac{arcsin ( \frac{21}{25} )}{2} + πn

2 x = arcsin (\frac{21}{25}) + 2 πn

Divide both sides by

2

2 x = arcsin (\frac{21}{25}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arcsin ( \frac{21}{25} )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{arcsin ( \frac{21}{25} )}{2} + πn

x = \frac{arcsin ( \frac{21}{25} )}{2} + πn

Solve

2 x = π - arcsin (\frac{21}{25}) + 2 πn : x = \frac{π}{2} - \frac{arcsin ( \frac{21}{25} )}{2} + πn

2 x = π - arcsin (\frac{21}{25}) + 2 πn

Divide both sides by

2

2 x = π - arcsin (\frac{21}{25}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{π}{2} - \frac{arcsin ( \frac{21}{25} )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{π}{2} - \frac{arcsin ( \frac{21}{25} )}{2} + πn

x = \frac{π}{2} - \frac{arcsin ( \frac{21}{25} )}{2} + πn

x = \frac{arcsin ( \frac{21}{25} )}{2} + πn, x = \frac{π}{2} - \frac{arcsin ( \frac{21}{25} )}{2} + πn

Show solutions in decimal form

x = \frac{0.99728 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.99728 \dots}{2} + πn

cot^{2} (x) cos (x) = cot^{2} (x)

4 sin^{2} (θ) - 8 cos (θ) + 1 = 0, 0 \leq θ < 2 π

4 sin (A) + 3 = 2 sin (A) + 4

0 = - 18 cos (3 x)

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

What is the general solution for sin(2x)= 21/25 ?
The general solution for sin(2x)= 21/25 is x=(0.99728…)/2+pin,x= pi/2-(0.99728…)/2+pin