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Popular Trigonometry >

sin(7.07t)=0.5

Solution

sin (7.07 t) = 0.5

Solution

t = \frac{50 π}{2121} + \frac{200 πn}{707}, t = \frac{250 π}{2121} + \frac{200 πn}{707}

Degrees

t = 4.24328 \dots^{\circ} + 50.91937 \dots^{\circ} n, t = 21.21640 \dots^{\circ} + 50.91937 \dots^{\circ} n

Solution steps

sin (7.07 t) = 0.5

General solutions for

sin (7.07 t) = 0.5

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}

7.07 t = \frac{π}{6} + 2 πn, 7.07 t = \frac{5 π}{6} + 2 πn

7.07 t = \frac{π}{6} + 2 πn, 7.07 t = \frac{5 π}{6} + 2 πn

Solve

7.07 t = \frac{π}{6} + 2 πn : t = \frac{50 π}{2121} + \frac{200 πn}{707}

7.07 t = \frac{π}{6} + 2 πn

Multiply both sides by

100

7.07 t = \frac{π}{6} + 2 πn

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

2

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

100

7.07 t \cdot 100 = \frac{π}{6} \cdot 100 + 2 πn \cdot 100

Refine

707 t = \frac{50 π}{3} + 200 πn

707 t = \frac{50 π}{3} + 200 πn

Divide both sides by

707

707 t = \frac{50 π}{3} + 200 πn

Divide both sides by

707

\frac{707 t}{707} = \frac{\frac{50 π}{3}}{707} + \frac{200 πn}{707}

Simplify

\frac{707 t}{707} = \frac{\frac{50 π}{3}}{707} + \frac{200 πn}{707}

Simplify

\frac{707 t}{707} : t

\frac{707 t}{707}

Divide the numbers:

\frac{707}{707} = 1

= t

Simplify

\frac{\frac{50 π}{3}}{707} + \frac{200 πn}{707} : \frac{50 π}{2121} + \frac{200 πn}{707}

\frac{\frac{50 π}{3}}{707} + \frac{200 πn}{707}

\frac{\frac{50 π}{3}}{707} = \frac{50 π}{2121}

\frac{\frac{50 π}{3}}{707}

Apply the fraction rule:

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

= \frac{50 π}{3 \cdot 707}

Multiply the numbers:

3 \cdot 707 = 2121

= \frac{50 π}{2121}

= \frac{50 π}{2121} + \frac{200 πn}{707}

t = \frac{50 π}{2121} + \frac{200 πn}{707}

t = \frac{50 π}{2121} + \frac{200 πn}{707}

t = \frac{50 π}{2121} + \frac{200 πn}{707}

Solve

7.07 t = \frac{5 π}{6} + 2 πn : t = \frac{250 π}{2121} + \frac{200 πn}{707}

7.07 t = \frac{5 π}{6} + 2 πn

Multiply both sides by

100

7.07 t = \frac{5 π}{6} + 2 πn

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

2

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

100

7.07 t \cdot 100 = \frac{5 π}{6} \cdot 100 + 2 πn \cdot 100

Refine

707 t = \frac{250 π}{3} + 200 πn

707 t = \frac{250 π}{3} + 200 πn

Divide both sides by

707

707 t = \frac{250 π}{3} + 200 πn

Divide both sides by

707

\frac{707 t}{707} = \frac{\frac{250 π}{3}}{707} + \frac{200 πn}{707}

Simplify

\frac{707 t}{707} = \frac{\frac{250 π}{3}}{707} + \frac{200 πn}{707}

Simplify

\frac{707 t}{707} : t

\frac{707 t}{707}

Divide the numbers:

\frac{707}{707} = 1

= t

Simplify

\frac{\frac{250 π}{3}}{707} + \frac{200 πn}{707} : \frac{250 π}{2121} + \frac{200 πn}{707}

\frac{\frac{250 π}{3}}{707} + \frac{200 πn}{707}

\frac{\frac{250 π}{3}}{707} = \frac{250 π}{2121}

\frac{\frac{250 π}{3}}{707}

Apply the fraction rule:

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

= \frac{250 π}{3 \cdot 707}

Multiply the numbers:

3 \cdot 707 = 2121

= \frac{250 π}{2121}

= \frac{250 π}{2121} + \frac{200 πn}{707}

t = \frac{250 π}{2121} + \frac{200 πn}{707}

t = \frac{250 π}{2121} + \frac{200 πn}{707}

t = \frac{250 π}{2121} + \frac{200 πn}{707}

t = \frac{50 π}{2121} + \frac{200 πn}{707}, t = \frac{250 π}{2121} + \frac{200 πn}{707}

Graph

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