What is the general solution for 5sin(pi/4 x)=4 ?

The general solution for 5sin(pi/4 x)=4 is x=(4*0.92729…)/pi+8n,x=4-(4*0.92729…)/pi+8n

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5sin(pi/4 x)=4

5 sin (\frac{π}{4} x) = 4

x = \frac{4 \cdot 0.92729 \dots}{π} + 8 n, x = 4 - \frac{4 \cdot 0.92729 \dots}{π} + 8 n

Solution steps

5 sin (\frac{π}{4} x) = 4

Divide both sides by

5

sin (\frac{π}{4} x) = \frac{4}{5}

Apply trig inverse properties

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

Solve

\frac{π}{4} x = arcsin (\frac{4}{5}) + 2 πn : x = \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n

Solve

\frac{π}{4} x = π - arcsin (\frac{4}{5}) + 2 πn : x = 4 - \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n

x = \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n, x = 4 - \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n

Show solutions in decimal form

x = \frac{4 \cdot 0.92729 \dots}{π} + 8 n, x = 4 - \frac{4 \cdot 0.92729 \dots}{π} + 8 n

1 - sec^{2} (θ) = tan^{2} (θ)

6 tan^{2} (x) = 5 sec (x)

x, cos^{2} (x) = 0.5

sin (x) = 0.24, 0 \leq x < 2 π

sec^{2} (θ) cot (θ) = 8

What is the general solution for 5sin(pi/4 x)=4 ?
The general solution for 5sin(pi/4 x)=4 is x=(4*0.92729…)/pi+8n,x=4-(4*0.92729…)/pi+8n