What is the general solution for 5sin(a)=4 ?

The general solution for 5sin(a)=4 is a=0.92729…+2pin,a=pi-0.92729…+2pin

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5sin(a)=4

5 sin (a) = 4

a = 0.92729 \dots + 2 πn, a = π - 0.92729 \dots + 2 πn

Degrees

a = 53.13010 \dots^{\circ} + 36 0^{\circ} n, a = 126.86989 \dots^{\circ} + 36 0^{\circ} n

Solution steps

5 sin (a) = 4

Divide both sides by

5

5 sin (a) = 4

Divide both sides by

5

\frac{5 sin ( a )}{5} = \frac{4}{5}

Simplify

sin (a) = \frac{4}{5}

sin (a) = \frac{4}{5}

Apply trig inverse properties

sin (a) = \frac{4}{5}

General solutions for

sin (a) = \frac{4}{5}

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

a = arcsin (\frac{4}{5}) + 2 πn, a = π - arcsin (\frac{4}{5}) + 2 πn

a = arcsin (\frac{4}{5}) + 2 πn, a = π - arcsin (\frac{4}{5}) + 2 πn

Show solutions in decimal form

a = 0.92729 \dots + 2 πn, a = π - 0.92729 \dots + 2 πn

2 cos^{4} (x) + 8 sin^{2} (x) = 5

cos^{4} (a) + cos^{2} (a) = 1

1 - cos (x) = 2 + cos (x)

(1 + cos (4 x)) sin (4 x) = 2 cos^{2} (2 x)

\frac{5 sin ( x ) + 6}{sin ( x )} = 17

What is the general solution for 5sin(a)=4 ?
The general solution for 5sin(a)=4 is a=0.92729…+2pin,a=pi-0.92729…+2pin