What is the general solution for (sin^2(x))/(cos(x))=16.33 ?

The general solution for (sin^2(x))/(cos(x))=16.33 is x=1.50974…+2pin,x=2pi-1.50974…+2pin

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(sin^2(x))/(cos(x))=16.33

\frac{sin ^{2} ( x )}{cos ( x )} = 16.33

x = 1.50974 \dots + 2 πn, x = 2 π - 1.50974 \dots + 2 πn

Solution steps

\frac{sin ^{2} ( x )}{cos ( x )} = 16.33

Subtract

16.33

from both sides

\frac{sin ^{2} ( x )}{cos ( x )} - 16.33 = 0

Rewrite using trig identities

- 16.33 + \frac{1 - cos ^{2} ( x )}{cos ( x )} = 0

Solve by substitution

cos (x) = - \frac{1633 + 2706689}{200}, cos (x) = \frac{2706689 - 1633}{200}

cos (x) = - \frac{1633 + 2706689}{200} :

No Solution

cos (x) = \frac{2706689 - 1633}{200} : x = arccos (\frac{2706689 - 1633}{200}) + 2 πn, x = 2 π - arccos (\frac{2706689 - 1633}{200}) + 2 πn

Combine all the solutions

x = arccos (\frac{2706689 - 1633}{200}) + 2 πn, x = 2 π - arccos (\frac{2706689 - 1633}{200}) + 2 πn

Show solutions in decimal form

x = 1.50974 \dots + 2 πn, x = 2 π - 1.50974 \dots + 2 πn

- 2 sin (θ) + 2 sin^{2} (θ) = 0

sin (2 π x) cos (π x) + cos (2 π x) sin (π x) = - 1

0 = - (sin (6.9256 - x) + (sin (- x)))

- 4 π^{2} sin (2 π x) = 0

- 9 sin (y) = 0

What is the general solution for (sin^2(x))/(cos(x))=16.33 ?
The general solution for (sin^2(x))/(cos(x))=16.33 is x=1.50974…+2pin,x=2pi-1.50974…+2pin