What is the general solution for 55^2=50^2+90^2-2*50*90*cos(x) ?

The general solution for 55^2=50^2+90^2-2*50*90*cos(x) is x=0.57043…+2pin,x=2pi-0.57043…+2pin

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Popular Trigonometry >

55^2=50^2+90^2-25090*cos(x)

Solution

5 5^{2} = 5 0^{2} + 9 0^{2} - 2 \cdot 50 \cdot 90 \cdot cos (x)

Solution

x = 0.57043 \dots + 2 πn, x = 2 π - 0.57043 \dots + 2 πn

Degrees

x = 32.68346 \dots^{\circ} + 36 0^{\circ} n, x = 327.31653 \dots^{\circ} + 36 0^{\circ} n

Solution steps

5 5^{2} = 5 0^{2} + 9 0^{2} - 2 \cdot 50 \cdot 90 cos (x)

Switch sides

5 0^{2} + 9 0^{2} - 2 \cdot 50 \cdot 90 cos (x) = 5 5^{2}

Multiply the numbers:

2 \cdot 50 \cdot 90 = 9000

5 0^{2} + 9 0^{2} - 9000 cos (x) = 5 5^{2}

5 0^{2} = 2500

2500 + 9 0^{2} - 9000 cos (x) = 5 5^{2}

9 0^{2} = 8100

2500 + 8100 - 9000 cos (x) = 5 5^{2}

Add the numbers:

2500 + 8100 = 10600

- 9000 cos (x) + 10600 = 5 5^{2}

5 5^{2} = 3025

- 9000 cos (x) + 10600 = 3025

Move

10600

to the right side

- 9000 cos (x) + 10600 = 3025

Subtract

10600

from both sides

- 9000 cos (x) + 10600 - 10600 = 3025 - 10600

Simplify

- 9000 cos (x) = - 7575

- 9000 cos (x) = - 7575

Divide both sides by

- 9000

- 9000 cos (x) = - 7575

Divide both sides by

- 9000

\frac{- 9000 cos ( x )}{- 9000} = \frac{- 7575}{- 9000}

Simplify

\frac{- 9000 cos ( x )}{- 9000} = \frac{- 7575}{- 9000}

Simplify

\frac{- 9000 cos ( x )}{- 9000} : cos (x)

\frac{- 9000 cos ( x )}{- 9000}

Apply the fraction rule:

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

= \frac{9000 cos ( x )}{9000}

Divide the numbers:

\frac{9000}{9000} = 1

= cos (x)

Simplify

\frac{- 7575}{- 9000} : \frac{101}{120}

\frac{- 7575}{- 9000}

Apply the fraction rule:

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

= \frac{7575}{9000}

Cancel the common factor:

75

= \frac{101}{120}

cos (x) = \frac{101}{120}

cos (x) = \frac{101}{120}

cos (x) = \frac{101}{120}

Apply trig inverse properties

cos (x) = \frac{101}{120}

General solutions for

cos (x) = \frac{101}{120}

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

x = arccos (\frac{101}{120}) + 2 πn, x = 2 π - arccos (\frac{101}{120}) + 2 πn

x = arccos (\frac{101}{120}) + 2 πn, x = 2 π - arccos (\frac{101}{120}) + 2 πn

Show solutions in decimal form

x = 0.57043 \dots + 2 πn, x = 2 π - 0.57043 \dots + 2 πn

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 55^2=50^2+90^2-2*50*90*cos(x) ?
The general solution for 55^2=50^2+90^2-2*50*90*cos(x) is x=0.57043…+2pin,x=2pi-0.57043…+2pin