What is the general solution for cos(0.5t+0.464)=1 ?

The general solution for cos(0.5t+0.464)=1 is t=4pin-116/125

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Popular Trigonometry >

cos(0.5t+0.464)=1

Solution

cos (0.5 t + 0.464) = 1

Solution

t = 4 πn - \frac{116}{125}

Degrees

t = - 53.17048 \dots^{\circ} + 72 0^{\circ} n

Solution steps

cos (0.5 t + 0.464) = 1

General solutions for

cos (0.5 t + 0.464) = 1

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

0.5 t + 0.464 = 0 + 2 πn

0.5 t + 0.464 = 0 + 2 πn

Solve

0.5 t + 0.464 = 0 + 2 πn : t = 4 πn - \frac{116}{125}

0.5 t + 0.464 = 0 + 2 πn

0 + 2 πn = 2 πn

0.5 t + 0.464 = 2 πn

Multiply both sides by

1000

0.5 t + 0.464 = 2 πn

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

3

digits to the right of the decimal point, therefore multiply by

1000

0.5 t \cdot 1000 + 0.464 \cdot 1000 = 2 πn \cdot 1000

Refine

500 t + 464 = 2000 πn

500 t + 464 = 2000 πn

Move

464

to the right side

500 t + 464 = 2000 πn

Subtract

464

from both sides

500 t + 464 - 464 = 2000 πn - 464

Simplify

500 t = 2000 πn - 464

500 t = 2000 πn - 464

Divide both sides by

500

500 t = 2000 πn - 464

Divide both sides by

500

\frac{500 t}{500} = \frac{2000 πn}{500} - \frac{464}{500}

Simplify

\frac{500 t}{500} = \frac{2000 πn}{500} - \frac{464}{500}

Simplify

\frac{500 t}{500} : t

\frac{500 t}{500}

Divide the numbers:

\frac{500}{500} = 1

= t

Simplify

\frac{2000 πn}{500} - \frac{464}{500} : 4 πn - \frac{116}{125}

\frac{2000 πn}{500} - \frac{464}{500}

Divide the numbers:

\frac{2000}{500} = 4

= 4 πn - \frac{464}{500}

Cancel

\frac{464}{500} : \frac{116}{125}

\frac{464}{500}

Cancel the common factor:

4

= \frac{116}{125}

= 4 πn - \frac{116}{125}

t = 4 πn - \frac{116}{125}

t = 4 πn - \frac{116}{125}

t = 4 πn - \frac{116}{125}

t = 4 πn - \frac{116}{125}

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for cos(0.5t+0.464)=1 ?
The general solution for cos(0.5t+0.464)=1 is t=4pin-116/125