What is the general solution for cos(x)=-7/(sqrt(14)\sqrt{5)} ?

The general solution for cos(x)=-7/(sqrt(14)\sqrt{5)} is x=2.56195…+2pin,x=-2.56195…+2pin

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cos(x)=-7/(sqrt(14)\sqrt{5)}

cos (x) = - \frac{7}{14 5}

x = 2.56195 \dots + 2 πn, x = - 2.56195 \dots + 2 πn

Radians

x = 2.56195 \dots + 6.28318 \dots n, x = - 2.56195 \dots + 6.28318 \dots n

Solution steps

cos (x) = - \frac{7}{14 5}

Simplify

- \frac{7}{14 5} : - \frac{7}{10}

- \frac{7}{14 5}

Cancel

\frac{7}{14 5} : \frac{7}{2 5}

\frac{7}{14 5}

Factor

14 : 27

Factor

14 = 2 \cdot 7

= 2 \cdot 7

Apply radical rule:

= 27

= \frac{7}{2 7 5}

Cancel

\frac{7}{2 7 5} : \frac{7}{2 5}

\frac{7}{2 7 5}

Apply radical rule:

7 = 7^{\frac{1}{2}}

= \frac{7}{2 \cdot 7 ^{\frac{1}{2}} 5}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{7 ^{1}}{7 ^{\frac{1}{2}}} = 7^{1 - \frac{1}{2}}

= \frac{7 ^{1 - \frac{1}{2}}}{2 5}

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{7 ^{\frac{1}{2}}}{2 5}

Apply radical rule:

7^{\frac{1}{2}} = 7

= \frac{7}{2 5}

= \frac{7}{2 5}

= - \frac{7}{2 5}

Simplify

25 : 10

25

Apply radical rule:

a b = a \cdot b

25 = 2 \cdot 5

= 2 \cdot 5

Multiply the numbers:

2 \cdot 5 = 10

= 10

= - \frac{7}{10}

Combine same powers :

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

= - \frac{7}{10}

Apply trig inverse properties

cos (x) = - \frac{7}{10}

General solutions for

cos (x) = - \frac{7}{10}

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

x = arccos (- \frac{7}{10}) + 2 πn, x = - arccos (- \frac{7}{10}) + 2 πn

x = arccos (- \frac{7}{10}) + 2 πn, x = - arccos (- \frac{7}{10}) + 2 πn

Show solutions in decimal form

x = 2.56195 \dots + 2 πn, x = - 2.56195 \dots + 2 πn

k, cos (k l) = 0

tan (2 x) = - \frac{- 270 - 120}{130}

3 tan (x + 4 3^{\circ}) = 2 cos (x + 4 3^{\circ})

\frac{sec ^{2} ( - 1 )}{tan ( x )} = tan (x)

4 sin (x) = 3 sec (x)

What is the general solution for cos(x)=-7/(sqrt(14)\sqrt{5)} ?
The general solution for cos(x)=-7/(sqrt(14)\sqrt{5)} is x=2.56195…+2pin,x=-2.56195…+2pin