What is the general solution for 1=8+7sin(15t) ?

The general solution for 1=8+7sin(15t) is t= pi/(10)+(2pin)/(15)

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1=8+7sin(15t)

Solution

1 = 8 + 7 sin (15 t)

Solution

t = \frac{π}{10} + \frac{2 πn}{15}

Degrees

t = 1 8^{\circ} + 2 4^{\circ} n

Solution steps

1 = 8 + 7 sin (15 t)

Switch sides

8 + 7 sin (15 t) = 1

Move

8

to the right side

8 + 7 sin (15 t) = 1

Subtract

8

from both sides

8 + 7 sin (15 t) - 8 = 1 - 8

Simplify

7 sin (15 t) = - 7

7 sin (15 t) = - 7

Divide both sides by

7

7 sin (15 t) = - 7

Divide both sides by

7

\frac{7 sin ( 15 t )}{7} = \frac{- 7}{7}

Simplify

sin (15 t) = - 1

sin (15 t) = - 1

General solutions for

sin (15 t) = - 1

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

15 t = \frac{3 π}{2} + 2 πn

15 t = \frac{3 π}{2} + 2 πn

Solve

15 t = \frac{3 π}{2} + 2 πn : t = \frac{π}{10} + \frac{2 πn}{15}

15 t = \frac{3 π}{2} + 2 πn

Divide both sides by

15

15 t = \frac{3 π}{2} + 2 πn

Divide both sides by

15

\frac{15 t}{15} = \frac{\frac{3 π}{2}}{15} + \frac{2 πn}{15}

Simplify

\frac{15 t}{15} = \frac{\frac{3 π}{2}}{15} + \frac{2 πn}{15}

Simplify

\frac{15 t}{15} : t

\frac{15 t}{15}

Divide the numbers:

\frac{15}{15} = 1

= t

Simplify

\frac{\frac{3 π}{2}}{15} + \frac{2 πn}{15} : \frac{π}{10} + \frac{2 πn}{15}

\frac{\frac{3 π}{2}}{15} + \frac{2 πn}{15}

\frac{\frac{3 π}{2}}{15} = \frac{π}{10}

\frac{\frac{3 π}{2}}{15}

Apply the fraction rule:

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

= \frac{3 π}{2 \cdot 15}

Multiply the numbers:

2 \cdot 15 = 30

= \frac{3 π}{30}

Cancel the common factor:

3

= \frac{π}{10}

= \frac{π}{10} + \frac{2 πn}{15}

t = \frac{π}{10} + \frac{2 πn}{15}

t = \frac{π}{10} + \frac{2 πn}{15}

t = \frac{π}{10} + \frac{2 πn}{15}

t = \frac{π}{10} + \frac{2 πn}{15}

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Frequently Asked Questions (FAQ)

What is the general solution for 1=8+7sin(15t) ?
The general solution for 1=8+7sin(15t) is t= pi/(10)+(2pin)/(15)