What is the general solution for cos(x)=(1-2)/(sqrt(26)) ?

The general solution for cos(x)=(1-2)/(sqrt(26)) is x=1.76819…+2pin,x=-1.76819…+2pin

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cos(x)=(1-2)/(sqrt(26))

cos (x) = \frac{1 - 2}{26}

x = 1.76819 \dots + 2 πn, x = - 1.76819 \dots + 2 πn

Radians

x = 1.76819 \dots + 6.28318 \dots n, x = - 1.76819 \dots + 6.28318 \dots n

Solution steps

cos (x) = \frac{1 - 2}{26}

Simplify

\frac{1 - 2}{26} : - \frac{26}{26}

\frac{1 - 2}{26}

Subtract the numbers:

1 - 2 = - 1

= \frac{- 1}{26}

Apply the fraction rule:

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

= - \frac{1}{26}

Rationalize

- \frac{1}{26} : - \frac{26}{26}

- \frac{1}{26}

Multiply by the conjugate

\frac{26}{26}

= - \frac{1 \cdot 26}{26 26}

1 \cdot 26 = 26

2626 = 26

2626

Apply radical rule:

a a = a

2626 = 26

= 26

= - \frac{26}{26}

= - \frac{26}{26}

cos (x) = - \frac{26}{26}

Apply trig inverse properties

cos (x) = - \frac{26}{26}

General solutions for

cos (x) = - \frac{26}{26}

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

x = arccos (- \frac{26}{26}) + 2 πn, x = - arccos (- \frac{26}{26}) + 2 πn

x = arccos (- \frac{26}{26}) + 2 πn, x = - arccos (- \frac{26}{26}) + 2 πn

Show solutions in decimal form

x = 1.76819 \dots + 2 πn, x = - 1.76819 \dots + 2 πn

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

cos (2 x) sin (x) + sin (x) = 5 cos (2 x) + 5

3 cot (θ) = 3

sec (x) = 1, - 2 π \leq x \leq 2 π

tan (t) = \frac{4}{3}, sin (t)

What is the general solution for cos(x)=(1-2)/(sqrt(26)) ?
The general solution for cos(x)=(1-2)/(sqrt(26)) is x=1.76819…+2pin,x=-1.76819…+2pin