What is the general solution for cos(x)=(4(1/2)-1)/3 ?

The general solution for cos(x)=(4(1/2)-1)/3 is x=1.23095…+2pin,x=2pi-1.23095…+2pin

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cos(x)=(4(1/2)-1)/3

cos (x) = \frac{4 ( \frac{1}{2} ) - 1}{3}

x = 1.23095 \dots + 2 πn, x = 2 π - 1.23095 \dots + 2 πn

Radians

x = 1.23095 \dots + 6.28318 \dots n, x = 5.05222 \dots + 6.28318 \dots n

Solution steps

cos (x) = \frac{4 ( \frac{1}{2} ) - 1}{3}

Simplify

\frac{4 \cdot \frac{1}{2} - 1}{3} : \frac{1}{3}

\frac{4 \cdot \frac{1}{2} - 1}{3}

4 \cdot \frac{1}{2} = 2

4 \cdot \frac{1}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 4}{2}

Multiply the numbers:

1 \cdot 4 = 4

= \frac{4}{2}

Divide the numbers:

\frac{4}{2} = 2

= 2

= \frac{2 - 1}{3}

Subtract the numbers:

2 - 1 = 1

= \frac{1}{3}

Apply trig inverse properties

cos (x) = \frac{1}{3}

General solutions for

cos (x) = \frac{1}{3}

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

x = arccos (\frac{1}{3}) + 2 πn, x = 2 π - arccos (\frac{1}{3}) + 2 πn

x = arccos (\frac{1}{3}) + 2 πn, x = 2 π - arccos (\frac{1}{3}) + 2 πn

Show solutions in decimal form

x = 1.23095 \dots + 2 πn, x = 2 π - 1.23095 \dots + 2 πn

sin (x) = \frac{π}{4} + \frac{0 π}{2}

cos (2 x) - sin (x) - 1 = 0

cos (x) = \frac{5}{20}

cos^{2} (x) + sin^{2} (x) = 2

sin (x) - 3 cos (x) = 1, 0 \leq x \leq 2 π

What is the general solution for cos(x)=(4(1/2)-1)/3 ?
The general solution for cos(x)=(4(1/2)-1)/3 is x=1.23095…+2pin,x=2pi-1.23095…+2pin