What is the general solution for 6sin(x)=10-7sin(x) ?

The general solution for 6sin(x)=10-7sin(x) is x=0.87763…+2pin,x=pi-0.87763…+2pin

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6sin(x)=10-7sin(x)

6 sin (x) = 10 - 7 sin (x)

x = 0.87763 \dots + 2 πn, x = π - 0.87763 \dots + 2 πn

Solution steps

6 sin (x) = 10 - 7 sin (x)

Solve by substitution

sin (x) = \frac{10}{13}

sin (x) = \frac{10}{13} : x = arcsin (\frac{10}{13}) + 2 πn, x = π - arcsin (\frac{10}{13}) + 2 πn

Combine all the solutions

x = arcsin (\frac{10}{13}) + 2 πn, x = π - arcsin (\frac{10}{13}) + 2 πn

Show solutions in decimal form

x = 0.87763 \dots + 2 πn, x = π - 0.87763 \dots + 2 πn

tan (x) = 1.35

tan (- y) = 0.9

cos (θ) = 3 sin (θ)

arctan (x + 1 x - 1) + arctan (x - 12) = arctan (2)

sin (α) = \frac{1}{4}

What is the general solution for 6sin(x)=10-7sin(x) ?
The general solution for 6sin(x)=10-7sin(x) is x=0.87763…+2pin,x=pi-0.87763…+2pin