What is the general solution for cos(θ)=(sqrt(75))/(10) ?

The general solution for cos(θ)=(sqrt(75))/(10) is θ= pi/6+2pin,θ=(11pi)/6+2pin

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cos(θ)=(sqrt(75))/(10)

cos (θ) = \frac{75}{10}

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

Solution steps

cos (θ) = \frac{75}{10}

Simplify

\frac{75}{10} : \frac{3}{2}

\frac{75}{10}

Factor

75 : 53

Factor

75 = 5^{2} \cdot 3

= 5^{2} \cdot 3

Apply radical rule:

= 3 5^{2}

Simplify

5^{2} : 5

5^{2}

Apply radical rule:

assuming

a \geq 0

= 5

= 53

Factor

10 : 2 \cdot 5

Factor

10 = 2 \cdot 5

= \frac{5 3}{2 \cdot 5}

Divide the numbers:

\frac{5}{5} = 1

= \frac{3}{2}

General solutions for

cos (θ) = \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}

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

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

tan (x) = \frac{50}{30}

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

cos (A) = \frac{1 ^{2} + 5. 2 ^{2} - 3.5}{2 ( 1 ) ( 5.2 )}

cos (5 x) - cos (3 x) = sin (4 x)

cos (9 0^{\circ} - x) + csc (x) = \frac{5}{2}

What is the general solution for cos(θ)=(sqrt(75))/(10) ?
The general solution for cos(θ)=(sqrt(75))/(10) is θ= pi/6+2pin,θ=(11pi)/6+2pin