What is the general solution for 69cos(T/2)=45 ?

The general solution for 69cos(T/2)=45 is T=2*0.86034…+4pin,T=4pi-2*0.86034…+4pin

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69cos(T/2)=45

Solution

69 cos (\frac{T}{2}) = 45

Solution

T = 2 \cdot 0.86034 \dots + 4 πn, T = 4 π - 2 \cdot 0.86034 \dots + 4 πn

Degrees

T = 98.58858 \dots^{\circ} + 72 0^{\circ} n, T = 621.41141 \dots^{\circ} + 72 0^{\circ} n

Solution steps

69 cos (\frac{T}{2}) = 45

Divide both sides by

69

69 cos (\frac{T}{2}) = 45

Divide both sides by

69

\frac{69 cos ( \frac{T}{2} )}{69} = \frac{45}{69}

Simplify

cos (\frac{T}{2}) = \frac{15}{23}

cos (\frac{T}{2}) = \frac{15}{23}

Apply trig inverse properties

cos (\frac{T}{2}) = \frac{15}{23}

General solutions for

cos (\frac{T}{2}) = \frac{15}{23}

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

\frac{T}{2} = arccos (\frac{15}{23}) + 2 πn, \frac{T}{2} = 2 π - arccos (\frac{15}{23}) + 2 πn

\frac{T}{2} = arccos (\frac{15}{23}) + 2 πn, \frac{T}{2} = 2 π - arccos (\frac{15}{23}) + 2 πn

Solve

\frac{T}{2} = arccos (\frac{15}{23}) + 2 πn : T = 2 arccos (\frac{15}{23}) + 4 πn

\frac{T}{2} = arccos (\frac{15}{23}) + 2 πn

Multiply both sides by

2

\frac{T}{2} = arccos (\frac{15}{23}) + 2 πn

Multiply both sides by

2

\frac{2 T}{2} = 2 arccos (\frac{15}{23}) + 2 \cdot 2 πn

Simplify

\frac{2 T}{2} = 2 arccos (\frac{15}{23}) + 2 \cdot 2 πn

Simplify

\frac{2 T}{2} : T

\frac{2 T}{2}

Divide the numbers:

\frac{2}{2} = 1

= T

Simplify

2 arccos (\frac{15}{23}) + 2 \cdot 2 πn : 2 arccos (\frac{15}{23}) + 4 πn

2 arccos (\frac{15}{23}) + 2 \cdot 2 πn

Multiply the numbers:

2 \cdot 2 = 4

= 2 arccos (\frac{15}{23}) + 4 πn

T = 2 arccos (\frac{15}{23}) + 4 πn

T = 2 arccos (\frac{15}{23}) + 4 πn

T = 2 arccos (\frac{15}{23}) + 4 πn

Solve

\frac{T}{2} = 2 π - arccos (\frac{15}{23}) + 2 πn : T = 4 π - 2 arccos (\frac{15}{23}) + 4 πn

\frac{T}{2} = 2 π - arccos (\frac{15}{23}) + 2 πn

Multiply both sides by

2

\frac{T}{2} = 2 π - arccos (\frac{15}{23}) + 2 πn

Multiply both sides by

2

\frac{2 T}{2} = 2 \cdot 2 π - 2 arccos (\frac{15}{23}) + 2 \cdot 2 πn

Simplify

\frac{2 T}{2} = 2 \cdot 2 π - 2 arccos (\frac{15}{23}) + 2 \cdot 2 πn

Simplify

\frac{2 T}{2} : T

\frac{2 T}{2}

Divide the numbers:

\frac{2}{2} = 1

= T

Simplify

2 \cdot 2 π - 2 arccos (\frac{15}{23}) + 2 \cdot 2 πn : 4 π - 2 arccos (\frac{15}{23}) + 4 πn

2 \cdot 2 π - 2 arccos (\frac{15}{23}) + 2 \cdot 2 πn

Multiply the numbers:

2 \cdot 2 = 4

= 4 π - 2 arccos (\frac{15}{23}) + 4 πn

T = 4 π - 2 arccos (\frac{15}{23}) + 4 πn

T = 4 π - 2 arccos (\frac{15}{23}) + 4 πn

T = 4 π - 2 arccos (\frac{15}{23}) + 4 πn

T = 2 arccos (\frac{15}{23}) + 4 πn, T = 4 π - 2 arccos (\frac{15}{23}) + 4 πn

Show solutions in decimal form

T = 2 \cdot 0.86034 \dots + 4 πn, T = 4 π - 2 \cdot 0.86034 \dots + 4 πn

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Frequently Asked Questions (FAQ)

What is the general solution for 69cos(T/2)=45 ?
The general solution for 69cos(T/2)=45 is T=2*0.86034…+4pin,T=4pi-2*0.86034…+4pin