What is the general solution for sin(x)-cos^2(x)=0 ?

The general solution for sin(x)-cos^2(x)=0 is x=0.66623…+2pin,x=pi-0.66623…+2pin

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sin(x)-cos^2(x)=0

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

x = 0.66623 \dots + 2 πn, x = π - 0.66623 \dots + 2 πn

Solution steps

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

Rewrite using trig identities

- 1 + sin (x) + sin^{2} (x) = 0

Solve by substitution

sin (x) = \frac{- 1 + 5}{2}, sin (x) = \frac{- 1 - 5}{2}

sin (x) = \frac{- 1 + 5}{2} : x = arcsin (\frac{- 1 + 5}{2}) + 2 πn, x = π - arcsin (\frac{- 1 + 5}{2}) + 2 πn

sin (x) = \frac{- 1 - 5}{2} :

No Solution

Combine all the solutions

x = arcsin (\frac{- 1 + 5}{2}) + 2 πn, x = π - arcsin (\frac{- 1 + 5}{2}) + 2 πn

Show solutions in decimal form

x = 0.66623 \dots + 2 πn, x = π - 0.66623 \dots + 2 πn

x, sin (x^{2}) + cos (y^{3}) = - 2

8 sin (12 0^{\circ} - x) = 9 sin (x)

cos (θ) = 0.625

x, sin (x) = 3 cos (x)

x, 1.12 = 0.04 sin (x)

What is the general solution for sin(x)-cos^2(x)=0 ?
The general solution for sin(x)-cos^2(x)=0 is x=0.66623…+2pin,x=pi-0.66623…+2pin