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Popular Trigonometry >

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

Solution

5.63 = 11 cos (\frac{2 π}{T} 0.137)

Solution

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

Degrees

T = 0^{\circ} + 6.74076 \dots^{\circ} n, T = 0^{\circ} + 4.27647 \dots^{\circ} n

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

11 cos (\frac{2 π}{T} 0.137) = 5.63

Divide both sides by

11

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

Simplify

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

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

Apply trig inverse properties

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

General solutions for

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

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

\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

\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}

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

Simplify

\frac{2 π}{T} \cdot 0.137 : \frac{0.274 π}{T}

\frac{2 π}{T} \cdot 0.137

Multiply fractions:

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

= \frac{2 π 0.137}{T}

Multiply the numbers:

2 \cdot 0.137 = 0.274

= \frac{0.274 π}{T}

\frac{0.274 π}{T} = arccos (0.51181 \dots) + 2 πn

Multiply both sides by

T

\frac{0.274 π}{T} = arccos (0.51181 \dots) + 2 πn

Multiply both sides by

T

\frac{0.274 π}{T} T = arccos (0.51181 \dots) T + 2 πn T

Simplify

0.274 π = arccos (0.51181 \dots) T + 2 πn T

0.274 π = arccos (0.51181 \dots) T + 2 πn T

Switch sides

arccos (0.51181 \dots) T + 2 πn T = 0.274 π

Factor

arccos (0.51181 \dots) T + 2 πn T : T (arccos (0.51181 \dots) + 2 πn)

arccos (0.51181 \dots) T + 2 πn T

Factor out common term

T

= T (arccos (0.51181 \dots) + 2 πn)

T (arccos (0.51181 \dots) + 2 πn) = 0.274 π

Divide both sides by

arccos (0.51181 \dots) + 2 πn; n \neq = - \frac{arccos ( 0.51181 \dots )}{2 π}

T (arccos (0.51181 \dots) + 2 πn) = 0.274 π

Divide both sides by

arccos (0.51181 \dots) + 2 πn; n \neq = - \frac{arccos ( 0.51181 \dots )}{2 π}

\frac{T ( arccos ( 0.51181 \dots ) + 2 πn )}{arccos ( 0.51181 \dots ) + 2 πn} = \frac{0.274 π}{arccos ( 0.51181 \dots ) + 2 πn}; n \neq = - \frac{arccos ( 0.51181 \dots )}{2 π}

Simplify

\frac{T ( arccos ( 0.51181 \dots ) + 2 πn )}{arccos ( 0.51181 \dots ) + 2 πn} = \frac{0.274 π}{arccos ( 0.51181 \dots ) + 2 πn}

Simplify

\frac{T ( arccos ( 0.51181 \dots ) + 2 πn )}{arccos ( 0.51181 \dots ) + 2 πn} : T

\frac{T ( arccos ( 0.51181 \dots ) + 2 πn )}{arccos ( 0.51181 \dots ) + 2 πn}

Cancel the common factor:

arccos (0.51181 \dots) + 2 πn

= T

Simplify

\frac{0.274 π}{arccos ( 0.51181 \dots ) + 2 πn} : \frac{0.86079 \dots}{1.03349 \dots + 6.28318 \dots n}

\frac{0.274 π}{arccos ( 0.51181 \dots ) + 2 πn}

arccos (0.51181 \dots) = 1.03349 \dots

= \frac{0.274 π}{1.03349 \dots + 2 πn}

Refine

= \frac{0.86079 \dots}{1.03349 \dots + 6.28318 \dots n}

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

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

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}

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

Simplify

\frac{2 π}{T} \cdot 0.137 : \frac{0.274 π}{T}

\frac{2 π}{T} \cdot 0.137

Multiply fractions:

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

= \frac{2 π 0.137}{T}

Multiply the numbers:

2 \cdot 0.137 = 0.274

= \frac{0.274 π}{T}

\frac{0.274 π}{T} = 2 π - arccos (0.51181 \dots) + 2 πn

Multiply both sides by

T

\frac{0.274 π}{T} = 2 π - arccos (0.51181 \dots) + 2 πn

Multiply both sides by

T

\frac{0.274 π}{T} T = 2 π T - arccos (0.51181 \dots) T + 2 πn T

Simplify

0.274 π = 2 π T - arccos (0.51181 \dots) T + 2 πn T

0.274 π = 2 π T - arccos (0.51181 \dots) T + 2 πn T

Switch sides

2 π T - arccos (0.51181 \dots) T + 2 πn T = 0.274 π

Factor

2 π T - arccos (0.51181 \dots) T + 2 πn T : T (2 π - arccos (0.51181 \dots) + 2 πn)

2 π T - arccos (0.51181 \dots) T + 2 πn T

Factor out common term

T

= T (2 π - arccos (0.51181 \dots) + 2 πn)

T (2 π - arccos (0.51181 \dots) + 2 πn) = 0.274 π

Divide both sides by

2 π - arccos (0.51181 \dots) + 2 πn; n \neq = \frac{- 2 π + arccos ( 0.51181 \dots )}{2 π}

T (2 π - arccos (0.51181 \dots) + 2 πn) = 0.274 π

Divide both sides by

2 π - arccos (0.51181 \dots) + 2 πn; n \neq = \frac{- 2 π + arccos ( 0.51181 \dots )}{2 π}

\frac{T ( 2 π - arccos ( 0.51181 \dots ) + 2 πn )}{2 π - arccos ( 0.51181 \dots ) + 2 πn} = \frac{0.274 π}{2 π - arccos ( 0.51181 \dots ) + 2 πn}; n \neq = \frac{- 2 π + arccos ( 0.51181 \dots )}{2 π}

Simplify

\frac{T ( 2 π - arccos ( 0.51181 \dots ) + 2 πn )}{2 π - arccos ( 0.51181 \dots ) + 2 πn} = \frac{0.274 π}{2 π - arccos ( 0.51181 \dots ) + 2 πn}

Simplify

\frac{T ( 2 π - arccos ( 0.51181 \dots ) + 2 πn )}{2 π - arccos ( 0.51181 \dots ) + 2 πn} : T

\frac{T ( 2 π - arccos ( 0.51181 \dots ) + 2 πn )}{2 π - arccos ( 0.51181 \dots ) + 2 πn}

Cancel the common factor:

2 π - arccos (0.51181 \dots) + 2 πn

= T

Simplify

\frac{0.274 π}{2 π - arccos ( 0.51181 \dots ) + 2 πn} : \frac{0.86079 \dots}{6.28318 \dots n + 5.24968 \dots}

\frac{0.274 π}{2 π - arccos ( 0.51181 \dots ) + 2 πn}

arccos (0.51181 \dots) = 1.03349 \dots

= \frac{0.274 π}{2 π - 1.03349 \dots + 2 πn}

Multiply the numbers:

0.274 \cdot 3.14159 \dots = 0.86079 \dots

= \frac{0.86079 \dots}{2 π - 1.03349 \dots + 2 πn}

Simplify

\frac{0.86079 \dots}{2 π - 1.03349 \dots + 2 πn}

Multiply the numbers:

2 \cdot 3.14159 \dots = 6.28318 \dots

= \frac{0.86079 \dots}{6.28318 \dots - 1.03349 \dots + 2 πn}

Multiply the numbers:

2 \cdot 3.14159 \dots = 6.28318 \dots

= \frac{0.86079 \dots}{6.28318 \dots - 1.03349 \dots + 6.28318 \dots n}

Subtract the numbers:

6.28318 \dots - 1.03349 \dots = 5.24968 \dots

= \frac{0.86079 \dots}{6.28318 \dots n + 5.24968 \dots}

= \frac{0.86079 \dots}{6.28318 \dots n + 5.24968 \dots}

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}{6.28318 \dots n + 5.24968 \dots}; n \neq = \frac{- 2 π + arccos ( 0.51181 \dots )}{2 π}

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}

Graph

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