What is the general solution for 4cos^2(x)+5sin(x)=3 ?

The general solution for 4cos^2(x)+5sin(x)=3 is x=-0.17630…+2pin,x=pi+0.17630…+2pin

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4cos^2(x)+5sin(x)=3

4 cos^{2} (x) + 5 sin (x) = 3

x = - 0.17630 \dots + 2 πn, x = π + 0.17630 \dots + 2 πn

Solution steps

4 cos^{2} (x) + 5 sin (x) = 3

Subtract

3

from both sides

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

Rewrite using trig identities

1 - 4 sin^{2} (x) + 5 sin (x) = 0

Solve by substitution

sin (x) = - \frac{- 5 + 41}{8}, sin (x) = \frac{5 + 41}{8}

sin (x) = - \frac{- 5 + 41}{8} : x = arcsin (- \frac{- 5 + 41}{8}) + 2 πn, x = π + arcsin (\frac{- 5 + 41}{8}) + 2 πn

sin (x) = \frac{5 + 41}{8} :

No Solution

Combine all the solutions

x = arcsin (- \frac{- 5 + 41}{8}) + 2 πn, x = π + arcsin (\frac{- 5 + 41}{8}) + 2 πn

Show solutions in decimal form

x = - 0.17630 \dots + 2 πn, x = π + 0.17630 \dots + 2 πn

cos^{4} (x) = cos^{4} (x) csc (x)

tan (θ) - 6 = - 2 - 3 tan (θ)

73500 = 130000 \cdot sin (x) + 0.15 \cdot 130000 \cdot cos (x)

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

tan (θ + 3 2^{\circ}) = cot (θ - 2 0^{\circ})

What is the general solution for 4cos^2(x)+5sin(x)=3 ?
The general solution for 4cos^2(x)+5sin(x)=3 is x=-0.17630…+2pin,x=pi+0.17630…+2pin