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Popular Trigonometry >

solvefor t,v=100cos(50t+20)v

Solution

solve for

t, v = 100 cos (50 t + 2 0^{\circ}) v

Solution

t = \frac{18 0 ^{\circ} n}{25} - 0. 4^{\circ} + \frac{1.56079 \dots}{50}, t = 7. 2^{\circ} - 0. 4^{\circ} + \frac{18 0 ^{\circ} n}{25} - \frac{1.56079 \dots}{50}

Radians

t = - \frac{π}{450} + \frac{1.56079 \dots}{50} + \frac{π}{25} n, t = \frac{π}{25} - \frac{π}{450} - \frac{1.56079 \dots}{50} + \frac{π}{25} n

Solution steps

v = 100 cos (50 t + 2 0^{\circ}) v

Switch sides

100 cos (50 t + \frac{π}{9}) v = v

Divide both sides by

100 v; v \neq = 0

100 cos (50 t + \frac{π}{9}) v = v

Divide both sides by

100 v; v \neq = 0

\frac{100 cos ( 50 t + \frac{π}{9} ) v}{100 v} = \frac{v}{100 v}; v \neq = 0

Simplify

cos (50 t + \frac{π}{9}) = \frac{1}{100}; v \neq = 0

cos (50 t + \frac{π}{9}) = \frac{1}{100}; v \neq = 0

Apply trig inverse properties

cos (50 t + 2 0^{\circ}) = \frac{1}{100}

General solutions for

cos (50 t + 2 0^{\circ}) = \frac{1}{100}

cos (x) = a \Rightarrow x = arccos (a) + 36 0^{\circ} n, x = 36 0^{\circ} - arccos (a) + 36 0^{\circ} n

50 t + 2 0^{\circ} = arccos (\frac{1}{100}) + 36 0^{\circ} n, 50 t + 2 0^{\circ} = 36 0^{\circ} - arccos (\frac{1}{100}) + 36 0^{\circ} n

50 t + 2 0^{\circ} = arccos (\frac{1}{100}) + 36 0^{\circ} n, 50 t + 2 0^{\circ} = 36 0^{\circ} - arccos (\frac{1}{100}) + 36 0^{\circ} n

Solve

50 t + 2 0^{\circ} = arccos (\frac{1}{100}) + 36 0^{\circ} n : t = \frac{18 0 ^{\circ} n}{25} - 0. 4^{\circ} + \frac{arccos ( \frac{1}{100} )}{50}

50 t + 2 0^{\circ} = arccos (\frac{1}{100}) + 36 0^{\circ} n

Move

2 0^{\circ}

to the right side

50 t + 2 0^{\circ} = arccos (\frac{1}{100}) + 36 0^{\circ} n

Subtract

2 0^{\circ}

from both sides

50 t + 2 0^{\circ} - 2 0^{\circ} = arccos (\frac{1}{100}) + 36 0^{\circ} n - 2 0^{\circ}

Simplify

50 t = arccos (\frac{1}{100}) + 36 0^{\circ} n - 2 0^{\circ}

50 t = arccos (\frac{1}{100}) + 36 0^{\circ} n - 2 0^{\circ}

Divide both sides by

50

50 t = arccos (\frac{1}{100}) + 36 0^{\circ} n - 2 0^{\circ}

Divide both sides by

50

\frac{50 t}{50} = \frac{arccos ( \frac{1}{100} )}{50} + \frac{36 0 ^{\circ} n}{50} - \frac{2 0 ^{\circ}}{50}

Simplify

\frac{50 t}{50} = \frac{arccos ( \frac{1}{100} )}{50} + \frac{36 0 ^{\circ} n}{50} - \frac{2 0 ^{\circ}}{50}

Simplify

\frac{50 t}{50} : t

\frac{50 t}{50}

Divide the numbers:

\frac{50}{50} = 1

= t

Simplify

\frac{arccos ( \frac{1}{100} )}{50} + \frac{36 0 ^{\circ} n}{50} - \frac{2 0 ^{\circ}}{50} : \frac{18 0 ^{\circ} n}{25} - 0. 4^{\circ} + \frac{arccos ( \frac{1}{100} )}{50}

\frac{arccos ( \frac{1}{100} )}{50} + \frac{36 0 ^{\circ} n}{50} - \frac{2 0 ^{\circ}}{50}

Group like terms

= \frac{36 0 ^{\circ} n}{50} - \frac{2 0 ^{\circ}}{50} + \frac{arccos ( \frac{1}{100} )}{50}

\frac{36 0 ^{\circ} n}{50} = \frac{18 0 ^{\circ} n}{25}

\frac{36 0 ^{\circ} n}{50}

Cancel the common factor:

2

= \frac{18 0 ^{\circ} n}{25}

\frac{2 0 ^{\circ}}{50} = 0. 4^{\circ}

\frac{2 0 ^{\circ}}{50}

Apply the fraction rule:

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

= \frac{18 0 ^{\circ}}{9 \cdot 50}

Multiply the numbers:

9 \cdot 50 = 450

= 0. 4^{\circ}

= \frac{18 0 ^{\circ} n}{25} - 0. 4^{\circ} + \frac{arccos ( \frac{1}{100} )}{50}

t = \frac{18 0 ^{\circ} n}{25} - 0. 4^{\circ} + \frac{arccos ( \frac{1}{100} )}{50}

t = \frac{18 0 ^{\circ} n}{25} - 0. 4^{\circ} + \frac{arccos ( \frac{1}{100} )}{50}

t = \frac{18 0 ^{\circ} n}{25} - 0. 4^{\circ} + \frac{arccos ( \frac{1}{100} )}{50}

Solve

50 t + 2 0^{\circ} = 36 0^{\circ} - arccos (\frac{1}{100}) + 36 0^{\circ} n : t = 7. 2^{\circ} - 0. 4^{\circ} + \frac{18 0 ^{\circ} n}{25} - \frac{arccos ( \frac{1}{100} )}{50}

50 t + 2 0^{\circ} = 36 0^{\circ} - arccos (\frac{1}{100}) + 36 0^{\circ} n

Move

2 0^{\circ}

to the right side

50 t + 2 0^{\circ} = 36 0^{\circ} - arccos (\frac{1}{100}) + 36 0^{\circ} n

Subtract

2 0^{\circ}

from both sides

50 t + 2 0^{\circ} - 2 0^{\circ} = 36 0^{\circ} - arccos (\frac{1}{100}) + 36 0^{\circ} n - 2 0^{\circ}

Simplify

50 t = 36 0^{\circ} - arccos (\frac{1}{100}) + 36 0^{\circ} n - 2 0^{\circ}

50 t = 36 0^{\circ} - arccos (\frac{1}{100}) + 36 0^{\circ} n - 2 0^{\circ}

Divide both sides by

50

50 t = 36 0^{\circ} - arccos (\frac{1}{100}) + 36 0^{\circ} n - 2 0^{\circ}

Divide both sides by

50

\frac{50 t}{50} = 7. 2^{\circ} - \frac{arccos ( \frac{1}{100} )}{50} + \frac{36 0 ^{\circ} n}{50} - \frac{2 0 ^{\circ}}{50}

Simplify

\frac{50 t}{50} = 7. 2^{\circ} - \frac{arccos ( \frac{1}{100} )}{50} + \frac{36 0 ^{\circ} n}{50} - \frac{2 0 ^{\circ}}{50}

Simplify

\frac{50 t}{50} : t

\frac{50 t}{50}

Divide the numbers:

\frac{50}{50} = 1

= t

Simplify

7. 2^{\circ} - \frac{arccos ( \frac{1}{100} )}{50} + \frac{36 0 ^{\circ} n}{50} - \frac{2 0 ^{\circ}}{50} : 7. 2^{\circ} - 0. 4^{\circ} + \frac{18 0 ^{\circ} n}{25} - \frac{arccos ( \frac{1}{100} )}{50}

7. 2^{\circ} - \frac{arccos ( \frac{1}{100} )}{50} + \frac{36 0 ^{\circ} n}{50} - \frac{2 0 ^{\circ}}{50}

Group like terms

= 7. 2^{\circ} + \frac{36 0 ^{\circ} n}{50} - \frac{2 0 ^{\circ}}{50} - \frac{arccos ( \frac{1}{100} )}{50}

7. 2^{\circ} = 7. 2^{\circ}

7. 2^{\circ}

Cancel the common factor:

2

= 7. 2^{\circ}

\frac{36 0 ^{\circ} n}{50} = \frac{18 0 ^{\circ} n}{25}

\frac{36 0 ^{\circ} n}{50}

Cancel the common factor:

2

= \frac{18 0 ^{\circ} n}{25}

\frac{2 0 ^{\circ}}{50} = 0. 4^{\circ}

\frac{2 0 ^{\circ}}{50}

Apply the fraction rule:

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

= \frac{18 0 ^{\circ}}{9 \cdot 50}

Multiply the numbers:

9 \cdot 50 = 450

= 0. 4^{\circ}

= 7. 2^{\circ} + \frac{18 0 ^{\circ} n}{25} - 0. 4^{\circ} - \frac{arccos ( \frac{1}{100} )}{50}

Group like terms

= 7. 2^{\circ} - 0. 4^{\circ} + \frac{18 0 ^{\circ} n}{25} - \frac{arccos ( \frac{1}{100} )}{50}

t = 7. 2^{\circ} - 0. 4^{\circ} + \frac{18 0 ^{\circ} n}{25} - \frac{arccos ( \frac{1}{100} )}{50}

t = 7. 2^{\circ} - 0. 4^{\circ} + \frac{18 0 ^{\circ} n}{25} - \frac{arccos ( \frac{1}{100} )}{50}

t = 7. 2^{\circ} - 0. 4^{\circ} + \frac{18 0 ^{\circ} n}{25} - \frac{arccos ( \frac{1}{100} )}{50}

t = \frac{18 0 ^{\circ} n}{25} - 0. 4^{\circ} + \frac{arccos ( \frac{1}{100} )}{50}, t = 7. 2^{\circ} - 0. 4^{\circ} + \frac{18 0 ^{\circ} n}{25} - \frac{arccos ( \frac{1}{100} )}{50}

Show solutions in decimal form

t = \frac{18 0 ^{\circ} n}{25} - 0. 4^{\circ} + \frac{1.56079 \dots}{50}, t = 7. 2^{\circ} - 0. 4^{\circ} + \frac{18 0 ^{\circ} n}{25} - \frac{1.56079 \dots}{50}

Graph

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