What is the general solution for 5cos(x)-4=0 ?

The general solution for 5cos(x)-4=0 is x=0.64350…+2pin,x=2pi-0.64350…+2pin

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5cos(x)-4=0

5 cos (x) - 4 = 0

x = 0.64350 \dots + 2 πn, x = 2 π - 0.64350 \dots + 2 πn

Degrees

x = 36.86989 \dots^{\circ} + 36 0^{\circ} n, x = 323.13010 \dots^{\circ} + 36 0^{\circ} n

Solution steps

5 cos (x) - 4 = 0

Move

4

to the right side

5 cos (x) - 4 = 0

Add

4

to both sides

5 cos (x) - 4 + 4 = 0 + 4

Simplify

5 cos (x) = 4

5 cos (x) = 4

Divide both sides by

5

5 cos (x) = 4

Divide both sides by

5

\frac{5 cos ( x )}{5} = \frac{4}{5}

Simplify

cos (x) = \frac{4}{5}

cos (x) = \frac{4}{5}

Apply trig inverse properties

cos (x) = \frac{4}{5}

General solutions for

cos (x) = \frac{4}{5}

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

x = arccos (\frac{4}{5}) + 2 πn, x = 2 π - arccos (\frac{4}{5}) + 2 πn

x = arccos (\frac{4}{5}) + 2 πn, x = 2 π - arccos (\frac{4}{5}) + 2 πn

Show solutions in decimal form

x = 0.64350 \dots + 2 πn, x = 2 π - 0.64350 \dots + 2 πn

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

sin (x) = 14

tan (x) = 0, 5

2 sec^{2} (x) - 5 sec (x) + 2 = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

2 sin (5 x) + 3 = 0, 0 \leq x \leq 2 π

What is the general solution for 5cos(x)-4=0 ?
The general solution for 5cos(x)-4=0 is x=0.64350…+2pin,x=2pi-0.64350…+2pin