What is the general solution for 15=25+2*sqrt(100)*cos(x) ?

The general solution for 15=25+2*sqrt(100)*cos(x) is x=(2pi)/3+2pin,x=(4pi)/3+2pin

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Popular Trigonometry >

15=25+2sqrt(100)cos(x)

Solution

15 = 25 + 2 \cdot 100 \cdot cos (x)

Solution

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Degrees

x = 12 0^{\circ} + 36 0^{\circ} n, x = 24 0^{\circ} + 36 0^{\circ} n

Solution steps

15 = 25 + 2100 cos (x)

Switch sides

25 + 2100 cos (x) = 15

2100 cos (x) = 20 cos (x)

2100 cos (x)

100 = 10

100

Factor the number:

100 = 1 0^{2}

= 1 0^{2}

Apply radical rule:

1 0^{2} = 10

= 10

= 2 \cdot 10 cos (x)

Multiply the numbers:

2 \cdot 10 = 20

= 20 cos (x)

25 + 20 cos (x) = 15

Move

25

to the right side

25 + 20 cos (x) = 15

Subtract

25

from both sides

25 + 20 cos (x) - 25 = 15 - 25

Simplify

20 cos (x) = - 10

20 cos (x) = - 10

Divide both sides by

20

20 cos (x) = - 10

Divide both sides by

20

\frac{20 cos ( x )}{20} = \frac{- 10}{20}

Simplify

\frac{20 cos ( x )}{20} = \frac{- 10}{20}

Simplify

\frac{20 cos ( x )}{20} : cos (x)

\frac{20 cos ( x )}{20}

Divide the numbers:

\frac{20}{20} = 1

= cos (x)

Simplify

\frac{- 10}{20} : - \frac{1}{2}

\frac{- 10}{20}

Apply the fraction rule:

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

= - \frac{10}{20}

Cancel the common factor:

10

= - \frac{1}{2}

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

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

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

General solutions for

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

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Graph

Popular Examples

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tan(2θ)=2.4

3sin^2(θ)=2sin(θ)+3

(sin(180)}{20}=\frac{sin(a))/8

(sin(x)+cos(x))^2=1^2

Frequently Asked Questions (FAQ)

What is the general solution for 15=25+2*sqrt(100)*cos(x) ?
The general solution for 15=25+2*sqrt(100)*cos(x) is x=(2pi)/3+2pin,x=(4pi)/3+2pin