What is the general solution for sin^2(x)=cos^3(x) ?

The general solution for sin^2(x)=cos^3(x) is x=0.71532…+2pin,x=2pi-0.71532…+2pin

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sin^2(x)=cos^3(x)

sin^{2} (x) = cos^{3} (x)

x = 0.71532 \dots + 2 πn, x = 2 π - 0.71532 \dots + 2 πn

Solution steps

sin^{2} (x) = cos^{3} (x)

Subtract

cos^{3} (x)

from both sides

sin^{2} (x) - cos^{3} (x) = 0

Rewrite using trig identities

1 - cos^{2} (x) - cos^{3} (x) = 0

Solve by substitution

cos (x) \approx 0.75487 \dots

cos (x) = 0.75487 \dots : x = arccos (0.75487 \dots) + 2 πn, x = 2 π - arccos (0.75487 \dots) + 2 πn

Combine all the solutions

x = arccos (0.75487 \dots) + 2 πn, x = 2 π - arccos (0.75487 \dots) + 2 πn

Show solutions in decimal form

x = 0.71532 \dots + 2 πn, x = 2 π - 0.71532 \dots + 2 πn

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sin^{2} (x) + sin^{6} (x) = 3 cos^{2} (2 x)

cot^{2} (x) - 7 cot (x) + 10 = 0

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What is the general solution for sin^2(x)=cos^3(x) ?
The general solution for sin^2(x)=cos^3(x) is x=0.71532…+2pin,x=2pi-0.71532…+2pin