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

The general solution for cos^2(t)-3sin(t)=3 is t=(3pi)/2+2pin

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cos^2(t)-3sin(t)=3

cos^{2} (t) - 3 sin (t) = 3

t = \frac{3 π}{2} + 2 πn

Solution steps

cos^{2} (t) - 3 sin (t) = 3

Subtract

3

from both sides

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

Rewrite using trig identities

- 2 - sin^{2} (t) - 3 sin (t) = 0

Solve by substitution

sin (t) = - 2, sin (t) = - 1

sin (t) = - 2 :

No Solution

sin (t) = - 1 : t = \frac{3 π}{2} + 2 πn

Combine all the solutions

t = \frac{3 π}{2} + 2 πn

4 sin^{4} (x) - 4 sin^{2} (x) + 1 = 0

4 sin (θ) + 23 = 0, 0^{\circ} \leq θ \leq 36 0^{\circ}

(1.33) sin (2 5^{\circ}) = (1.5) sin (θ)

cos (y) = - \frac{1}{2}

\frac{2}{1 + sin ( x )} = 3 - 2 sin (x)

What is the general solution for cos^2(t)-3sin(t)=3 ?
The general solution for cos^2(t)-3sin(t)=3 is t=(3pi)/2+2pin