What is the general solution for solvefor x,sqrt(2)*sqrt(2.25)*cos(x)=0 ?

The general solution for solvefor x,sqrt(2)*sqrt(2.25)*cos(x)=0 is x= pi/2+2pin,x=(3pi)/2+2pin

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solvefor x,sqrt(2)sqrt(2.25)cos(x)=0

solve for

x, 2 \cdot 2.25 \cdot cos (x) = 0

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

Solution steps

2 2.25 cos (x) = 0

Simplify

2 2.25 : 4.5

2 2.25

Apply radical rule:

a b = a \cdot b

2 2.25 = 2 \cdot 2.25

= 2 \cdot 2.25

Multiply the numbers:

2 \cdot 2.25 = 4.5

= 4.5

4.5 cos (x) = 0

Divide both sides by

4.5

4.5 cos (x) = 0

Divide both sides by

4.5

\frac{4.5 cos ( x )}{4.5} = \frac{0}{4.5}

Simplify

cos (x) = 0

cos (x) = 0

General solutions for

cos (x) = 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}

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

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

x, 2 sin (x) = 1

cot (x) + 2 cos (x) = 0

2 cot (θ) - 1 = 2, cot (θ) - 1 = 0

2 cos^{2} (a) - 7 cos (a) + 3 = 0

y, x = 2 cos (2 y)

What is the general solution for solvefor x,sqrt(2)*sqrt(2.25)*cos(x)=0 ?
The general solution for solvefor x,sqrt(2)*sqrt(2.25)*cos(x)=0 is x= pi/2+2pin,x=(3pi)/2+2pin