5.63=11cos((2pi)/T 0.137)

Solution

5.63 = 11 cos (\frac{2 π}{T} 0.137)

T = \frac{0.86079 \dots}{1.03349 \dots + 6.28318 \dots n}, T = \frac{0.86079 \dots}{6.28318 \dots n + 5.24968 \dots}

Solution steps

5.63 = 11 cos (\frac{2 π}{T} \cdot 0.137)

Switch sides

11 cos (\frac{2 π}{T} \cdot 0.137) = 5.63

Divide both sides by

11

cos (\frac{2 π}{T} 0.137) = 0.51181 \dots

Apply trig inverse properties

\frac{2 π}{T} \cdot 0.137 = arccos (0.51181 \dots) + 2 πn, \frac{2 π}{T} \cdot 0.137 = 2 π - arccos (0.51181 \dots) + 2 πn

Solve

\frac{2 π}{T} \cdot 0.137 = arccos (0.51181 \dots) + 2 πn : T = \frac{0.86079 \dots}{1.03349 \dots + 6.28318 \dots n}; n \neq = - \frac{arccos ( 0.51181 \dots )}{2 π}

Solve

\frac{2 π}{T} \cdot 0.137 = 2 π - arccos (0.51181 \dots) + 2 πn : T = \frac{0.86079 \dots}{6.28318 \dots n + 5.24968 \dots}; n \neq = \frac{- 2 π + arccos ( 0.51181 \dots )}{2 π}

T = \frac{0.86079 \dots}{1.03349 \dots + 6.28318 \dots n}, T = \frac{0.86079 \dots}{6.28318 \dots n + 5.24968 \dots}

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