What is the general solution for cos(x)=(sqrt(34))/(sqrt(70)) ?

The general solution for cos(x)=(sqrt(34))/(sqrt(70)) is x=0.79968…+2pin,x=2pi-0.79968…+2pin

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cos(x)=(sqrt(34))/(sqrt(70))

cos (x) = \frac{34}{70}

x = 0.79968 \dots + 2 πn, x = 2 π - 0.79968 \dots + 2 πn

Radians

x = 0.79968 \dots + 6.28318 \dots n, x = 5.48349 \dots + 6.28318 \dots n

Solution steps

cos (x) = \frac{34}{70}

Simplify

\frac{34}{70} : \frac{17}{35}

\frac{34}{70}

Factor

34 : 217

Factor

34 = 2 \cdot 17

= 2 \cdot 17

Apply radical rule:

n ab = n a n b

= 217

Factor

70 : 257

Factor

70 = 2 \cdot 5 \cdot 7

= 2 \cdot 5 \cdot 7

Apply radical rule:

n ab = n a n b

= 257

= \frac{2 17}{2 5 7}

Cancel the common factor:

2

= \frac{17}{5 7}

Simplify

57 : 35

57

Apply radical rule:

a b = a \cdot b

57 = 5 \cdot 7

= 5 \cdot 7

Multiply the numbers:

5 \cdot 7 = 35

= 35

= \frac{17}{35}

Combine same powers :

\frac{x}{y} = \frac{x}{y}

= \frac{17}{35}

Apply trig inverse properties

cos (x) = \frac{17}{35}

General solutions for

cos (x) = \frac{17}{35}

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

x = arccos (\frac{17}{35}) + 2 πn, x = 2 π - arccos (\frac{17}{35}) + 2 πn

x = arccos (\frac{17}{35}) + 2 πn, x = 2 π - arccos (\frac{17}{35}) + 2 πn

Show solutions in decimal form

x = 0.79968 \dots + 2 πn, x = 2 π - 0.79968 \dots + 2 πn

What is the general solution for cos(x)=(sqrt(34))/(sqrt(70)) ?
The general solution for cos(x)=(sqrt(34))/(sqrt(70)) is x=0.79968…+2pin,x=2pi-0.79968…+2pin