What is the general solution for solvefor x,sin(x)+y^2=4 ?

The general solution for solvefor x,sin(x)+y^2=4 is x=arcsin(4-y^2)+2pin,x=pi+arcsin(-4+y^2)+2pin

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solvefor x,sin(x)+y^2=4

solve for

x, sin (x) + y^{2} = 4

x = arcsin (4 - y^{2}) + 2 πn, x = π + arcsin (- 4 + y^{2}) + 2 πn

Solution steps

sin (x) + y^{2} = 4

Move

y^{2}

to the right side

sin (x) + y^{2} = 4

Subtract

y^{2}

from both sides

sin (x) + y^{2} - y^{2} = 4 - y^{2}

Simplify

sin (x) = 4 - y^{2}

sin (x) = 4 - y^{2}

Apply trig inverse properties

sin (x) = 4 - y^{2}

General solutions for

sin (x) = 4 - y^{2}

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

x = arcsin (4 - y^{2}) + 2 πn, x = π + arcsin (- 4 + y^{2}) + 2 πn

x = arcsin (4 - y^{2}) + 2 πn, x = π + arcsin (- 4 + y^{2}) + 2 πn

4 tan^{2} (θ) = - 3 tan (θ) + tan^{2} (θ)

2 sec^{2} (x) - 3 tan (x) = 11

3 cos (2 x) = - 3

4 cos^{2} (θ) + cos (2 θ) - 7 cos (θ) = - 2

cos (θ) = \frac{4 2}{7}

What is the general solution for solvefor x,sin(x)+y^2=4 ?
The general solution for solvefor x,sin(x)+y^2=4 is x=arcsin(4-y^2)+2pin,x=pi+arcsin(-4+y^2)+2pin