What is the general solution for 4cos(x)-5=-8 ?

The general solution for 4cos(x)-5=-8 is x=2.41885…+2pin,x=-2.41885…+2pin

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4cos(x)-5=-8

4 cos (x) - 5 = - 8

x = 2.41885 \dots + 2 πn, x = - 2.41885 \dots + 2 πn

Degrees

x = 138.59037 \dots^{\circ} + 36 0^{\circ} n, x = - 138.59037 \dots^{\circ} + 36 0^{\circ} n

Solution steps

4 cos (x) - 5 = - 8

Move

5

to the right side

4 cos (x) - 5 = - 8

Add

5

to both sides

4 cos (x) - 5 + 5 = - 8 + 5

Simplify

4 cos (x) = - 3

4 cos (x) = - 3

Divide both sides by

4

4 cos (x) = - 3

Divide both sides by

4

\frac{4 cos ( x )}{4} = \frac{- 3}{4}

Simplify

cos (x) = - \frac{3}{4}

cos (x) = - \frac{3}{4}

Apply trig inverse properties

cos (x) = - \frac{3}{4}

General solutions for

cos (x) = - \frac{3}{4}

cos (x) = - a \Rightarrow x = arccos (- a) + 2 πn, x = - arccos (- a) + 2 πn

x = arccos (- \frac{3}{4}) + 2 πn, x = - arccos (- \frac{3}{4}) + 2 πn

x = arccos (- \frac{3}{4}) + 2 πn, x = - arccos (- \frac{3}{4}) + 2 πn

Show solutions in decimal form

x = 2.41885 \dots + 2 πn, x = - 2.41885 \dots + 2 πn

sin (x) + 4 csc (x) + 5 = 0, 0 \leq x \leq 2 π

r = a sin (3 x)

sin (x) = \frac{18}{25}

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

x, cos (x) = \frac{1}{4}

What is the general solution for 4cos(x)-5=-8 ?
The general solution for 4cos(x)-5=-8 is x=2.41885…+2pin,x=-2.41885…+2pin