What is the general solution for 4cos(x)-3=0 ?

The general solution for 4cos(x)-3=0 is x=0.72273…+2pin,x=2pi-0.72273…+2pin

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4cos(x)-3=0

4 cos (x) - 3 = 0

x = 0.72273 \dots + 2 πn, x = 2 π - 0.72273 \dots + 2 πn

Degrees

x = 41.40962 \dots^{\circ} + 36 0^{\circ} n, x = 318.59037 \dots^{\circ} + 36 0^{\circ} n

Solution steps

4 cos (x) - 3 = 0

Move

3

to the right side

4 cos (x) - 3 = 0

Add

3

to both sides

4 cos (x) - 3 + 3 = 0 + 3

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 = 2 π - arccos (a) + 2 πn

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

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

Show solutions in decimal form

x = 0.72273 \dots + 2 πn, x = 2 π - 0.72273 \dots + 2 πn

cos (θ) cos (2 θ) + sin (θ) sin (2 θ) = \frac{1}{2}

8 sin (x) tan (x) + tan (x) = 0

sin (x) - 3 = cos (x) - 3

sin (x) + 4 csc (x) + 5 = 0

sin (x) = \frac{5}{9}

What is the general solution for 4cos(x)-3=0 ?
The general solution for 4cos(x)-3=0 is x=0.72273…+2pin,x=2pi-0.72273…+2pin