What is the general solution for 6/5 arccos(y/6)=pi ?

The general solution for 6/5 arccos(y/6)=pi is y=-3sqrt(3)

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6/5 arccos(y/6)=pi

\frac{6}{5} arccos (\frac{y}{6}) = π

y = - 33

Solution steps

\frac{6}{5} arccos (\frac{y}{6}) = π

Multiply both sides by

5

\frac{6}{5} arccos (\frac{y}{6}) = π

Multiply both sides by

5

5 \cdot \frac{6}{5} arccos (\frac{y}{6}) = 5 π

Simplify

6 arccos (\frac{y}{6}) = 5 π

6 arccos (\frac{y}{6}) = 5 π

Divide both sides by

6

6 arccos (\frac{y}{6}) = 5 π

Divide both sides by

6

\frac{6 arccos ( \frac{y}{6} )}{6} = \frac{5 π}{6}

Simplify

arccos (\frac{y}{6}) = \frac{5 π}{6}

arccos (\frac{y}{6}) = \frac{5 π}{6}

Apply trig inverse properties

arccos (\frac{y}{6}) = \frac{5 π}{6}

arccos (x) = a \Rightarrow x = cos (a)

\frac{y}{6} = cos (\frac{5 π}{6})

cos (\frac{5 π}{6}) = - \frac{3}{2}

cos (\frac{5 π}{6})

Use the following trivial identity:

cos (\frac{5 π}{6}) = - \frac{3}{2}

cos (\frac{5 π}{6})

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{3}{2}

= - \frac{3}{2}

\frac{y}{6} = - \frac{3}{2}

\frac{y}{6} = - \frac{3}{2}

Solve

\frac{y}{6} = - \frac{3}{2} : y = - 33

\frac{y}{6} = - \frac{3}{2}

Multiply both sides by

6

\frac{y}{6} = - \frac{3}{2}

Multiply both sides by

6

\frac{6 y}{6} = 6 (- \frac{3}{2})

Simplify

\frac{6 y}{6} = 6 (- \frac{3}{2})

Simplify

\frac{6 y}{6} : y

\frac{6 y}{6}

Divide the numbers:

\frac{6}{6} = 1

= y

Simplify

6 (- \frac{3}{2}) : - 33

6 (- \frac{3}{2})

Remove parentheses:

(- a) = - a

= - 6 \cdot \frac{3}{2}

Multiply fractions:

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

= - \frac{3 \cdot 6}{2}

Divide the numbers:

\frac{6}{2} = 3

= - 33

y = - 33

y = - 33

y = - 33

y = - 33

cos (x) = \frac{154}{212.85}

4 sin^{2} (x) - 2 = 0, 0 \leq x \leq 2 π

csc^{2} (θ) = 7 cot (θ) + 9

cos^{2} (x) + 6 cos (x) = - 3, y = 3

2 sec^{2} (x) - 5 tan (x) = 5

What is the general solution for 6/5 arccos(y/6)=pi ?
The general solution for 6/5 arccos(y/6)=pi is y=-3sqrt(3)