What is the general solution for -5pisin((pi(t))/2)=7.071 ?

The general solution for -5pisin((pi(t))/2)=7.071 is t=-(2*0.46693…)/pi+4n,t=2+(2*0.46693…)/pi+4n

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-5pisin((pi(t))/2)=7.071

- 5 π sin (\frac{π ( t )}{2}) = 7.071

t = - \frac{2 \cdot 0.46693 \dots}{π} + 4 n, t = 2 + \frac{2 \cdot 0.46693 \dots}{π} + 4 n

Solution steps

- 5 π sin (\frac{π ( t )}{2}) = 7.071

Divide both sides by

- 5 π

sin (\frac{π t}{2}) = - 0.45015 \dots

Apply trig inverse properties

\frac{π t}{2} = arcsin (- 0.45015 \dots) + 2 πn, \frac{π t}{2} = π + arcsin (0.45015 \dots) + 2 πn

Solve

\frac{π t}{2} = arcsin (- 0.45015 \dots) + 2 πn : t = - \frac{2 arcsin ( 0.45015 \dots )}{π} + 4 n

Solve

\frac{π t}{2} = π + arcsin (0.45015 \dots) + 2 πn : t = 2 + \frac{2 arcsin ( 0.45015 \dots )}{π} + 4 n

t = - \frac{2 arcsin ( 0.45015 \dots )}{π} + 4 n, t = 2 + \frac{2 arcsin ( 0.45015 \dots )}{π} + 4 n

Show solutions in decimal form

t = - \frac{2 \cdot 0.46693 \dots}{π} + 4 n, t = 2 + \frac{2 \cdot 0.46693 \dots}{π} + 4 n

9.8 \cdot sin (x) - 19.6 \cdot cos (x) = 4.7

cos (x) = - 3 sin (x)

sin (α) = \frac{3}{5}, 0 < a < \frac{π}{2}

- \frac{15 ( 0.5 cos ( x ) - sin ( x ) )}{( 0.5 sin ( x ) + cos ( x ) ) ^{2}} = 0

x, 0.33 = sin (209.42 x)

What is the general solution for -5pisin((pi(t))/2)=7.071 ?
The general solution for -5pisin((pi(t))/2)=7.071 is t=-(2*0.46693…)/pi+4n,t=2+(2*0.46693…)/pi+4n