What is the general solution for 1.5=1+0.6cos((pit)/2) ?

The general solution for 1.5=1+0.6cos((pit)/2) is t=(2*0.58568…)/pi+4n,t=4-(2*0.58568…)/pi+4n

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1.5=1+0.6cos((pit)/2)

1.5 = 1 + 0.6 cos (\frac{π t}{2})

t = \frac{2 \cdot 0.58568 \dots}{π} + 4 n, t = 4 - \frac{2 \cdot 0.58568 \dots}{π} + 4 n

Solution steps

1.5 = 1 + 0.6 cos (\frac{π t}{2})

Switch sides

1 + 0.6 cos (\frac{π t}{2}) = 1.5

Multiply both sides by

10

10 + 6 cos (\frac{π t}{2}) = 15

Move

10

to the right side

6 cos (\frac{π t}{2}) = 5

Divide both sides by

6

cos (\frac{π t}{2}) = \frac{5}{6}

Apply trig inverse properties

\frac{π t}{2} = arccos (\frac{5}{6}) + 2 πn, \frac{π t}{2} = 2 π - arccos (\frac{5}{6}) + 2 πn

Solve

\frac{π t}{2} = arccos (\frac{5}{6}) + 2 πn : t = \frac{2 arccos ( \frac{5}{6} )}{π} + 4 n

Solve

\frac{π t}{2} = 2 π - arccos (\frac{5}{6}) + 2 πn : t = 4 - \frac{2 arccos ( \frac{5}{6} )}{π} + 4 n

t = \frac{2 arccos ( \frac{5}{6} )}{π} + 4 n, t = 4 - \frac{2 arccos ( \frac{5}{6} )}{π} + 4 n

Show solutions in decimal form

t = \frac{2 \cdot 0.58568 \dots}{π} + 4 n, t = 4 - \frac{2 \cdot 0.58568 \dots}{π} + 4 n

tan (x) csc (x) = cos (2)

x, z = e^{y} sin (x) y

tan (θ) sec (θ) = cot (θ) csc (θ)

0 = 4 + 3 cos (x)

cos^{2} (x) - cos (x) = 0.75

What is the general solution for 1.5=1+0.6cos((pit)/2) ?
The general solution for 1.5=1+0.6cos((pit)/2) is t=(2*0.58568…)/pi+4n,t=4-(2*0.58568…)/pi+4n