What is the general solution for 400=812.25+400-1140cos(a) ?

The general solution for 400=812.25+400-1140cos(a) is a=0.77774…+2pin,a=2pi-0.77774…+2pin

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Popular >

400=812.25+400-1140cos(a)

Solution

400 = 812.25 + 400 - 1140 cos (a)

Solution

a = 0.77774 \dots + 2 πn, a = 2 π - 0.77774 \dots + 2 πn

Degrees

a = 44.56131 \dots^{\circ} + 36 0^{\circ} n, a = 315.43868 \dots^{\circ} + 36 0^{\circ} n

Solution steps

400 = 812.25 + 400 - 1140 cos (a)

Switch sides

812.25 + 400 - 1140 cos (a) = 400

Subtract

400

from both sides

812.25 + 400 - 1140 cos (a) - 400 = 400 - 400

Simplify

812.25 - 1140 cos (a) = 0

Move

812.25

to the right side

812.25 - 1140 cos (a) = 0

Subtract

812.25

from both sides

812.25 - 1140 cos (a) - 812.25 = 0 - 812.25

Simplify

- 1140 cos (a) = - 812.25

- 1140 cos (a) = - 812.25

Divide both sides by

- 1140

- 1140 cos (a) = - 812.25

Divide both sides by

- 1140

\frac{- 1140 cos ( a )}{- 1140} = \frac{- 812.25}{- 1140}

Simplify

\frac{- 1140 cos ( a )}{- 1140} = \frac{- 812.25}{- 1140}

Simplify

\frac{- 1140 cos ( a )}{- 1140} : cos (a)

\frac{- 1140 cos ( a )}{- 1140}

Apply the fraction rule:

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

= \frac{1140 cos ( a )}{1140}

Divide the numbers:

\frac{1140}{1140} = 1

= cos (a)

Simplify

\frac{- 812.25}{- 1140} : 0.7125

\frac{- 812.25}{- 1140}

Apply the fraction rule:

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

= \frac{812.25}{1140}

Divide the numbers:

\frac{812.25}{1140} = 0.7125

= 0.7125

cos (a) = 0.7125

cos (a) = 0.7125

cos (a) = 0.7125

Apply trig inverse properties

cos (a) = 0.7125

General solutions for

cos (a) = 0.7125

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

a = arccos (0.7125) + 2 πn, a = 2 π - arccos (0.7125) + 2 πn

a = arccos (0.7125) + 2 πn, a = 2 π - arccos (0.7125) + 2 πn

Show solutions in decimal form

a = 0.77774 \dots + 2 πn, a = 2 π - 0.77774 \dots + 2 πn

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Frequently Asked Questions (FAQ)

What is the general solution for 400=812.25+400-1140cos(a) ?
The general solution for 400=812.25+400-1140cos(a) is a=0.77774…+2pin,a=2pi-0.77774…+2pin