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sin(7.07t)=0.5

해법

sin (7.07 t) = 0.5

해법

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

도

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

솔루션 단계

sin (7.07 t) = 0.5

일반 솔루션

sin (7.07 t) = 0.5

sin (x)

주기율표

2 πn

주기:

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

7.07 t = \frac{π}{6} + 2 πn

해결 :

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

7.07 t = \frac{π}{6} + 2 πn

양쪽을 곱한 값

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

다듬다

707 t = \frac{50 π}{3} + 200 πn

707 t = \frac{50 π}{3} + 200 πn

양쪽을 다음으로 나눕니다

707

707 t = \frac{50 π}{3} + 200 πn

양쪽을 다음으로 나눕니다

707

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

단순화

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

\frac{707 t}{707}

간소화하다 :

t

\frac{707 t}{707}

숫자를 나눕니다:

\frac{707}{707} = 1

= t

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

간소화하다 :

\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}

분수 규칙 적용:

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

= \frac{50 π}{3 \cdot 707}

숫자를 곱하시오:

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}

7.07 t = \frac{5 π}{6} + 2 πn

해결 :

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

7.07 t = \frac{5 π}{6} + 2 πn

양쪽을 곱한 값

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

다듬다

707 t = \frac{250 π}{3} + 200 πn

707 t = \frac{250 π}{3} + 200 πn

양쪽을 다음으로 나눕니다

707

707 t = \frac{250 π}{3} + 200 πn

양쪽을 다음으로 나눕니다

707

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

단순화

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

\frac{707 t}{707}

간소화하다 :

t

\frac{707 t}{707}

숫자를 나눕니다:

\frac{707}{707} = 1

= t

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

간소화하다 :

\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}

분수 규칙 적용:

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

= \frac{250 π}{3 \cdot 707}

숫자를 곱하시오:

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}

해법

해법

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