What is the general solution for 3=7cos(pi/3 t) ?

The general solution for 3=7cos(pi/3 t) is t=(3*1.12788…)/pi+6n,t=6-(3*1.12788…)/pi+6n

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3=7cos(pi/3 t)

3 = 7 cos (\frac{π}{3} t)

t = \frac{3 \cdot 1.12788 \dots}{π} + 6 n, t = 6 - \frac{3 \cdot 1.12788 \dots}{π} + 6 n

Solution steps

3 = 7 cos (\frac{π}{3} t)

Switch sides

7 cos (\frac{π}{3} t) = 3

Divide both sides by

7

cos (\frac{π}{3} t) = \frac{3}{7}

Apply trig inverse properties

\frac{π}{3} t = arccos (\frac{3}{7}) + 2 πn, \frac{π}{3} t = 2 π - arccos (\frac{3}{7}) + 2 πn

Solve

\frac{π}{3} t = arccos (\frac{3}{7}) + 2 πn : t = \frac{3 arccos ( \frac{3}{7} )}{π} + 6 n

Solve

\frac{π}{3} t = 2 π - arccos (\frac{3}{7}) + 2 πn : t = 6 - \frac{3 arccos ( \frac{3}{7} )}{π} + 6 n

t = \frac{3 arccos ( \frac{3}{7} )}{π} + 6 n, t = 6 - \frac{3 arccos ( \frac{3}{7} )}{π} + 6 n

Show solutions in decimal form

t = \frac{3 \cdot 1.12788 \dots}{π} + 6 n, t = 6 - \frac{3 \cdot 1.12788 \dots}{π} + 6 n

cos^{2} (2 x) = cos (4 x)

θ, tan (2 θ) = - 1

3 cos (z + 1.2) = 2

\frac{1}{2} = \frac{3}{2} \cdot cos (x)

cos (\frac{x}{2}) = - 12

What is the general solution for 3=7cos(pi/3 t) ?
The general solution for 3=7cos(pi/3 t) is t=(3*1.12788…)/pi+6n,t=6-(3*1.12788…)/pi+6n