What is the general solution for cos(θ/4)=(sqrt(2))/2 ?

The general solution for cos(θ/4)=(sqrt(2))/2 is θ=pi+8pin,θ=7pi+8pin

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Popular >

cos(θ/4)=(sqrt(2))/2

Solution

cos (\frac{θ}{4}) = \frac{2}{2}

Solution

θ = π + 8 πn, θ = 7 π + 8 πn

Degrees

θ = 18 0^{\circ} + 144 0^{\circ} n, θ = 126 0^{\circ} + 144 0^{\circ} n

Solution steps

cos (\frac{θ}{4}) = \frac{2}{2}

General solutions for

cos (\frac{θ}{4}) = \frac{2}{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}

\frac{θ}{4} = \frac{π}{4} + 2 πn, \frac{θ}{4} = \frac{7 π}{4} + 2 πn

\frac{θ}{4} = \frac{π}{4} + 2 πn, \frac{θ}{4} = \frac{7 π}{4} + 2 πn

Solve

\frac{θ}{4} = \frac{π}{4} + 2 πn : θ = π + 8 πn

\frac{θ}{4} = \frac{π}{4} + 2 πn

Multiply both sides by

4

\frac{θ}{4} = \frac{π}{4} + 2 πn

Multiply both sides by

4

\frac{4 θ}{4} = 4 \cdot \frac{π}{4} + 4 \cdot 2 πn

Simplify

\frac{4 θ}{4} = 4 \cdot \frac{π}{4} + 4 \cdot 2 πn

Simplify

\frac{4 θ}{4} : θ

\frac{4 θ}{4}

Divide the numbers:

\frac{4}{4} = 1

= θ

Simplify

4 \cdot \frac{π}{4} + 4 \cdot 2 πn : π + 8 πn

4 \cdot \frac{π}{4} + 4 \cdot 2 πn

4 \cdot \frac{π}{4} = π

4 \cdot \frac{π}{4}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{π 4}{4}

Cancel the common factor:

4

= π

4 \cdot 2 πn = 8 πn

4 \cdot 2 πn

Multiply the numbers:

4 \cdot 2 = 8

= 8 πn

= π + 8 πn

θ = π + 8 πn

θ = π + 8 πn

θ = π + 8 πn

Solve

\frac{θ}{4} = \frac{7 π}{4} + 2 πn : θ = 7 π + 8 πn

\frac{θ}{4} = \frac{7 π}{4} + 2 πn

Multiply both sides by

4

\frac{θ}{4} = \frac{7 π}{4} + 2 πn

Multiply both sides by

4

\frac{4 θ}{4} = 4 \cdot \frac{7 π}{4} + 4 \cdot 2 πn

Simplify

\frac{4 θ}{4} = 4 \cdot \frac{7 π}{4} + 4 \cdot 2 πn

Simplify

\frac{4 θ}{4} : θ

\frac{4 θ}{4}

Divide the numbers:

\frac{4}{4} = 1

= θ

Simplify

4 \cdot \frac{7 π}{4} + 4 \cdot 2 πn : 7 π + 8 πn

4 \cdot \frac{7 π}{4} + 4 \cdot 2 πn

4 \cdot \frac{7 π}{4} = 7 π

4 \cdot \frac{7 π}{4}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{7 π 4}{4}

Cancel the common factor:

4

= 7 π

4 \cdot 2 πn = 8 πn

4 \cdot 2 πn

Multiply the numbers:

4 \cdot 2 = 8

= 8 πn

= 7 π + 8 πn

θ = 7 π + 8 πn

θ = 7 π + 8 πn

θ = 7 π + 8 πn

θ = π + 8 πn, θ = 7 π + 8 πn

Popular Examples

cot(x-2)=-(sqrt(3))/3

cot (x - 2) = - \frac{3}{3}

cosh(x)+4sinh(x)+2=0

cosh (x) + 4 sinh (x) + 2 = 0

cos(b)= 5/13

cos (b) = \frac{5}{13}

solvefor x,sin(x)= 1/3 solve for

x, sin (x) = \frac{1}{3}

tan(A)= 5/12

tan (A) = \frac{5}{12}

Frequently Asked Questions (FAQ)

What is the general solution for cos(θ/4)=(sqrt(2))/2 ?
The general solution for cos(θ/4)=(sqrt(2))/2 is θ=pi+8pin,θ=7pi+8pin