What is the general solution for 5cos(x)=1 ?

The general solution for 5cos(x)=1 is x=1.36943…+2pin,x=2pi-1.36943…+2pin

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5cos(x)=1

5 cos (x) = 1

x = 1.36943 \dots + 2 πn, x = 2 π - 1.36943 \dots + 2 πn

Degrees

x = 78.46304 \dots^{\circ} + 36 0^{\circ} n, x = 281.53695 \dots^{\circ} + 36 0^{\circ} n

Solution steps

5 cos (x) = 1

Divide both sides by

5

5 cos (x) = 1

Divide both sides by

5

\frac{5 cos ( x )}{5} = \frac{1}{5}

Simplify

cos (x) = \frac{1}{5}

cos (x) = \frac{1}{5}

Apply trig inverse properties

cos (x) = \frac{1}{5}

General solutions for

cos (x) = \frac{1}{5}

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

x = arccos (\frac{1}{5}) + 2 πn, x = 2 π - arccos (\frac{1}{5}) + 2 πn

x = arccos (\frac{1}{5}) + 2 πn, x = 2 π - arccos (\frac{1}{5}) + 2 πn

Show solutions in decimal form

x = 1.36943 \dots + 2 πn, x = 2 π - 1.36943 \dots + 2 πn

cos (θ) = \frac{2}{11}

3 cos (x) + 5 = 7, 0 \leq x \leq 2 π

9 sin (\frac{x}{2}) + 9 cos (x) = 0

- 5 cos (x) + 5 sin (x) = \frac{5 2}{2}

10 sin (θ) = 4 cos^{2} (θ) + 2

What is the general solution for 5cos(x)=1 ?
The general solution for 5cos(x)=1 is x=1.36943…+2pin,x=2pi-1.36943…+2pin