What is the general solution for cos^2(x)+3sin(x)+1=0 ?

The general solution for cos^2(x)+3sin(x)+1=0 is x=-0.59626…+2pin,x=pi+0.59626…+2pin

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cos^2(x)+3sin(x)+1=0

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

x = - 0.59626 \dots + 2 πn, x = π + 0.59626 \dots + 2 πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

sin (x) = - \frac{- 3 + 17}{2}, sin (x) = \frac{3 + 17}{2}

sin (x) = - \frac{- 3 + 17}{2} : x = arcsin (- \frac{- 3 + 17}{2}) + 2 πn, x = π + arcsin (\frac{- 3 + 17}{2}) + 2 πn

sin (x) = \frac{3 + 17}{2} :

No Solution

Combine all the solutions

x = arcsin (- \frac{- 3 + 17}{2}) + 2 πn, x = π + arcsin (\frac{- 3 + 17}{2}) + 2 πn

Show solutions in decimal form

x = - 0.59626 \dots + 2 πn, x = π + 0.59626 \dots + 2 πn

\frac{a ^{0.2}}{( cos ^{2} ( x ) ) - cos ^{2} ( x ) - 1} = 0

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

4 cos^{2} (x) + 17 sin (x) = 8

cos^{4} (x) = 1 - 8 sin^{2} (x) cos^{2} (x)

tan (x) = \frac{10}{18}

What is the general solution for cos^2(x)+3sin(x)+1=0 ?
The general solution for cos^2(x)+3sin(x)+1=0 is x=-0.59626…+2pin,x=pi+0.59626…+2pin