What is the general solution for cos(x)= 3/(sqrt(10)) ?

The general solution for cos(x)= 3/(sqrt(10)) is x=0.32175…+2pin,x=2pi-0.32175…+2pin

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cos(x)= 3/(sqrt(10))

cos (x) = \frac{3}{10}

x = 0.32175 \dots + 2 πn, x = 2 π - 0.32175 \dots + 2 πn

Radians

x = 0.32175 \dots + 6.28318 \dots n, x = 5.96143 \dots + 6.28318 \dots n

Solution steps

cos (x) = \frac{3}{10}

Simplify

\frac{3}{10} : \frac{3 10}{10}

\frac{3}{10}

Multiply by the conjugate

\frac{10}{10}

= \frac{3 10}{10 10}

1010 = 10

1010

Apply radical rule:

a a = a

1010 = 10

= 10

= \frac{3 10}{10}

cos (x) = \frac{3 10}{10}

Apply trig inverse properties

cos (x) = \frac{3 10}{10}

General solutions for

cos (x) = \frac{3 10}{10}

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

x = arccos (\frac{3 10}{10}) + 2 πn, x = 2 π - arccos (\frac{3 10}{10}) + 2 πn

x = arccos (\frac{3 10}{10}) + 2 πn, x = 2 π - arccos (\frac{3 10}{10}) + 2 πn

Show solutions in decimal form

x = 0.32175 \dots + 2 πn, x = 2 π - 0.32175 \dots + 2 πn

cos (θ) + 3 sin (θ) = 1

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

6 tan (x) - 23 = 0

sec (θ) = \frac{5}{4}

2 cos^{3} (x) - cos^{2} (x) = cos (x)

What is the general solution for cos(x)= 3/(sqrt(10)) ?
The general solution for cos(x)= 3/(sqrt(10)) is x=0.32175…+2pin,x=2pi-0.32175…+2pin