What is the general solution for 3cos^2(x)+5sin(x)-1=0 ?

The general solution for 3cos^2(x)+5sin(x)-1=0 is x=-0.33983…+2pin,x=pi+0.33983…+2pin

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3cos^2(x)+5sin(x)-1=0

3 cos^{2} (x) + 5 sin (x) - 1 = 0

x = - 0.33983 \dots + 2 πn, x = π + 0.33983 \dots + 2 πn

Solution steps

3 cos^{2} (x) + 5 sin (x) - 1 = 0

Rewrite using trig identities

2 - 3 sin^{2} (x) + 5 sin (x) = 0

Solve by substitution

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

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

sin (x) = 2 :

No Solution

Combine all the solutions

x = arcsin (- \frac{1}{3}) + 2 πn, x = π + arcsin (\frac{1}{3}) + 2 πn

Show solutions in decimal form

x = - 0.33983 \dots + 2 πn, x = π + 0.33983 \dots + 2 πn

2 cos^{2} (θ) = 7 cos (θ) - 3

sin (θ) = (\frac{173}{210})

\frac{3 tan ^{2} ( x ) - 5}{cos ( x ) + 1} = 0

sin (3 x) = \frac{1}{2}, 0 \leq x \leq 2 π

cos (θ) = sec (θ), 0 \leq θ < 2 π

What is the general solution for 3cos^2(x)+5sin(x)-1=0 ?
The general solution for 3cos^2(x)+5sin(x)-1=0 is x=-0.33983…+2pin,x=pi+0.33983…+2pin