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

The general solution for 3sin(x)+cos^2(x)=2 is x=0.39192…+2pin,x=pi-0.39192…+2pin

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

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

x = 0.39192 \dots + 2 πn, x = π - 0.39192 \dots + 2 πn

Solution steps

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

Subtract

2

from both sides

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

Rewrite using trig identities

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

Solve by substitution

sin (x) = \frac{3 - 5}{2}, sin (x) = \frac{3 + 5}{2}

sin (x) = \frac{3 - 5}{2} : x = arcsin (\frac{3 - 5}{2}) + 2 πn, x = π - arcsin (\frac{3 - 5}{2}) + 2 πn

sin (x) = \frac{3 + 5}{2} :

No Solution

Combine all the solutions

x = arcsin (\frac{3 - 5}{2}) + 2 πn, x = π - arcsin (\frac{3 - 5}{2}) + 2 πn

Show solutions in decimal form

x = 0.39192 \dots + 2 πn, x = π - 0.39192 \dots + 2 πn

5 sin (2 θ) - 7 sin (θ) = 0

cos (θ) = \frac{3}{3}

arctan (x + 1) + arctan (x - 1) = arctan (2)

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

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

What is the general solution for 3sin(x)+cos^2(x)=2 ?
The general solution for 3sin(x)+cos^2(x)=2 is x=0.39192…+2pin,x=pi-0.39192…+2pin