What is the general solution for solvefor y,2cos(5x+y)=0 ?

The general solution for solvefor y,2cos(5x+y)=0 is y= pi/2+2pin-5x,y=(3pi)/2+2pin-5x

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solvefor y,2cos(5x+y)=0

solve for

y, 2 cos (5 x + y) = 0

y = \frac{π}{2} + 2 πn - 5 x, y = \frac{3 π}{2} + 2 πn - 5 x

Solution steps

2 cos (5 x + y) = 0

Divide both sides by

2

2 cos (5 x + y) = 0

Divide both sides by

2

\frac{2 cos ( 5 x + y )}{2} = \frac{0}{2}

Simplify

cos (5 x + y) = 0

cos (5 x + y) = 0

General solutions for

cos (5 x + y) = 0

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}

5 x + y = \frac{π}{2} + 2 πn, 5 x + y = \frac{3 π}{2} + 2 πn

5 x + y = \frac{π}{2} + 2 πn, 5 x + y = \frac{3 π}{2} + 2 πn

Solve

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

5 x + y = \frac{π}{2} + 2 πn

Move

5 x

to the right side

5 x + y = \frac{π}{2} + 2 πn

Subtract

5 x

from both sides

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

Simplify

y = \frac{π}{2} + 2 πn - 5 x

y = \frac{π}{2} + 2 πn - 5 x

Solve

5 x + y = \frac{3 π}{2} + 2 πn : y = \frac{3 π}{2} + 2 πn - 5 x

5 x + y = \frac{3 π}{2} + 2 πn

Move

5 x

to the right side

5 x + y = \frac{3 π}{2} + 2 πn

Subtract

5 x

from both sides

5 x + y - 5 x = \frac{3 π}{2} + 2 πn - 5 x

Simplify

y = \frac{3 π}{2} + 2 πn - 5 x

y = \frac{3 π}{2} + 2 πn - 5 x

y = \frac{π}{2} + 2 πn - 5 x, y = \frac{3 π}{2} + 2 πn - 5 x

2 cos^{2} (x) + 15 sin (x) - 15 = 0

cos (2 x) = sin (x), - 2 π \leq x \leq 2 π

5 sec^{2} (θ) sin (θ) - cos (θ) = 0

cos (x) = \frac{8}{11}

4 sec (θ) - 3 = 3 + 7 sec (θ)

What is the general solution for solvefor y,2cos(5x+y)=0 ?
The general solution for solvefor y,2cos(5x+y)=0 is y= pi/2+2pin-5x,y=(3pi)/2+2pin-5x