What is the general solution for cos(x+5)= 1/2 sqrt(3),0<= x<= 2pi ?

The general solution for cos(x+5)= 1/2 sqrt(3),0<= x<= 2pi is x=(11pi-30)/6 ,x=(13pi-30)/6

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cos(x+5)= 1/2 sqrt(3),0<= x<= 2pi

cos (x + 5) = \frac{1}{2} 3, 0 \leq x \leq 2 π

x = \frac{11 π - 30}{6}, x = \frac{13 π - 30}{6}

Solution steps

cos (x + 5) = \frac{1}{2} 3, 0 \leq x \leq 2 π

Simplify

\frac{1}{2} 3 : \frac{3}{2}

\frac{1}{2} 3

Multiply fractions:

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

= \frac{1 \cdot 3}{2}

Multiply:

1 \cdot 3 = 3

= \frac{3}{2}

General solutions for

cos (x + 5) = \frac{3}{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 + 5 = \frac{π}{6} + 2 πn, x + 5 = \frac{11 π}{6} + 2 πn

x + 5 = \frac{π}{6} + 2 πn, x + 5 = \frac{11 π}{6} + 2 πn

Solve

x + 5 = \frac{π}{6} + 2 πn : x = \frac{π}{6} + 2 πn - 5

x + 5 = \frac{π}{6} + 2 πn

Move

5

to the right side

x + 5 = \frac{π}{6} + 2 πn

Subtract

5

from both sides

x + 5 - 5 = \frac{π}{6} + 2 πn - 5

Simplify

x = \frac{π}{6} + 2 πn - 5

x = \frac{π}{6} + 2 πn - 5

Solve

x + 5 = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{6} + 2 πn - 5

x + 5 = \frac{11 π}{6} + 2 πn

Move

5

to the right side

x + 5 = \frac{11 π}{6} + 2 πn

Subtract

5

from both sides

x + 5 - 5 = \frac{11 π}{6} + 2 πn - 5

Simplify

x = \frac{11 π}{6} + 2 πn - 5

x = \frac{11 π}{6} + 2 πn - 5

x = \frac{π}{6} + 2 πn - 5, x = \frac{11 π}{6} + 2 πn - 5

Solutions for the range

0 \leq x \leq 2 π

x = \frac{11 π - 30}{6}, x = \frac{13 π - 30}{6}

cos^{2} (x) = 3 sin^{2} (x)

2 sec^{2} (x) + 3 sec (x) - 2 = 0

- 4 arctan (x) = π

sin^{2} (x) = sin (x) cos (x)

sin (x) = - \frac{3}{2}, 0 \leq x \leq 2 π

What is the general solution for cos(x+5)= 1/2 sqrt(3),0<= x<= 2pi ?
The general solution for cos(x+5)= 1/2 sqrt(3),0<= x<= 2pi is x=(11pi-30)/6 ,x=(13pi-30)/6