What is the general solution for cos(x)=(13^2+18^2-28^2)/(2*13*18) ?

The general solution for cos(x)=(13^2+18^2-28^2)/(2*13*18) is x=2.24182…+2pin,x=-2.24182…+2pin

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cos(x)=(13^2+18^2-28^2)/(21318)

cos (x) = \frac{1 3 ^{2} + 1 8 ^{2} - 2 8 ^{2}}{2 \cdot 13 \cdot 18}

x = 2.24182 \dots + 2 πn, x = - 2.24182 \dots + 2 πn

Radians

x = 2.24182 \dots + 6.28318 \dots n, x = - 2.24182 \dots + 6.28318 \dots n

Solution steps

cos (x) = \frac{1 3 ^{2} + 1 8 ^{2} - 2 8 ^{2}}{2 \cdot 13 \cdot 18}

Simplify

\frac{1 3 ^{2} + 1 8 ^{2} - 2 8 ^{2}}{2 \cdot 13 \cdot 18} : - \frac{97}{156}

\frac{1 3 ^{2} + 1 8 ^{2} - 2 8 ^{2}}{2 \cdot 13 \cdot 18}

1 3^{2} + 1 8^{2} - 2 8^{2} = - 291

1 3^{2} + 1 8^{2} - 2 8^{2}

1 3^{2} = 169

= 169 + 1 8^{2} - 2 8^{2}

1 8^{2} = 324

= 169 + 324 - 2 8^{2}

2 8^{2} = 784

= 169 + 324 - 784

Add/Subtract the numbers:

169 + 324 - 784 = - 291

= - 291

= \frac{- 291}{2 \cdot 13 \cdot 18}

Multiply the numbers:

2 \cdot 13 \cdot 18 = 468

= \frac{- 291}{468}

Apply the fraction rule:

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

= - \frac{291}{468}

Cancel the common factor:

3

= - \frac{97}{156}

Apply trig inverse properties

cos (x) = - \frac{97}{156}

General solutions for

cos (x) = - \frac{97}{156}

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

x = arccos (- \frac{97}{156}) + 2 πn, x = - arccos (- \frac{97}{156}) + 2 πn

x = arccos (- \frac{97}{156}) + 2 πn, x = - arccos (- \frac{97}{156}) + 2 πn

Show solutions in decimal form

x = 2.24182 \dots + 2 πn, x = - 2.24182 \dots + 2 πn

0.16085 = sin (\frac{2 π}{365} (x - 114))

sin (x) = - \frac{8}{17}, π \leq x \leq \frac{3 π}{2}, sin (2 x)

tan (θ) cos (2 7^{\circ}) = cos (6 3^{\circ})

3 - sin (x) = cos (2 x)

cot^{2} (x) - cot (x) - 2 = 0

What is the general solution for cos(x)=(13^2+18^2-28^2)/(2*13*18) ?
The general solution for cos(x)=(13^2+18^2-28^2)/(2*13*18) is x=2.24182…+2pin,x=-2.24182…+2pin