What is the general solution for 4sin(t/2)-1=1,-pi/2 <= t<= pi/2 ?

The general solution for 4sin(t/2)-1=1,-pi/2 <= t<= pi/2 is t= pi/3

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4sin(t/2)-1=1,-pi/2 <= t<= pi/2

4 sin (\frac{t}{2}) - 1 = 1, - \frac{π}{2} \leq t \leq \frac{π}{2}

t = \frac{π}{3}

Solution steps

4 sin (\frac{t}{2}) - 1 = 1, - \frac{π}{2} \leq t \leq \frac{π}{2}

Move

1

to the right side

4 sin (\frac{t}{2}) = 2

Divide both sides by

4

sin (\frac{t}{2}) = \frac{1}{2}

General solutions for

sin (\frac{t}{2}) = \frac{1}{2}

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

Solve

\frac{t}{2} = \frac{π}{6} + 2 πn : t = \frac{π}{3} + 4 πn

Solve

\frac{t}{2} = \frac{5 π}{6} + 2 πn : t = \frac{5 π}{3} + 4 πn

t = \frac{π}{3} + 4 πn, t = \frac{5 π}{3} + 4 πn

Solutions for the range

- \frac{π}{2} \leq t \leq \frac{π}{2}

t = \frac{π}{3}

- 6 cos (θ) - 10 = - 7

sin^{2} (x) = cos^{2} (x) + 1

tanh (x) = 1

tan (θ) = \frac{1}{3}

sin (θ) = \frac{20}{29}

What is the general solution for 4sin(t/2)-1=1,-pi/2 <= t<= pi/2 ?
The general solution for 4sin(t/2)-1=1,-pi/2 <= t<= pi/2 is t= pi/3