What is the general solution for cos(x)=sqrt(9/10) ?

The general solution for cos(x)=sqrt(9/10) is x=0.32175…+2pin,x=2pi-0.32175…+2pin

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cos(x)=sqrt(9/10)

cos (x) = \frac{9}{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{9}{10}

Simplify

\frac{9}{10} : \frac{3 10}{10}

\frac{9}{10}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \frac{9}{10}

9 = 3

9

Factor the number:

9 = 3^{2}

= 3^{2}

Apply radical rule:

3^{2} = 3

= 3

= \frac{3}{10}

Rationalize

\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}

= \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

34 \cdot sin (\frac{π}{6} (x - 4.3)) = 34

2 (sin (x)) 2 - 5 cos (x) - 4 = 0

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

0 = cos^{2} (x) + sin^{2} (x) - 2 sin (x), 0 \leq x \leq 2 π

sin (θ) = - \frac{7}{25}, sin (2 θ)

What is the general solution for cos(x)=sqrt(9/10) ?
The general solution for cos(x)=sqrt(9/10) is x=0.32175…+2pin,x=2pi-0.32175…+2pin