Solve the trigonometric equation in the interval [0, 2𝜋). Give the exact value, if possible; otherwise, round your answer to two decimal places. (Enter your answers as a comma-separated list.)

Question

Solve the trigonometric equation in the interval [0, 2𝜋).

 Give the exact value, if possible; otherwise, round your answer to two decimal places. (Enter your answers as a comma-separated list.)

7 sin(𝜃) − 4 = 0

Answer 1

7 sin(𝜃) − 4 = 0 Isolate the sin to one side of the equation. Add 4 and divide by 7.

sin(𝜃) = 4/7 This value is not on the unit circle. So we need to use the calculator.

𝜃 = sin ^-1 (4/7)

𝜃 = 0.61 (Make sure the calculator is in radians)

This is one solution. On the interval given, sin would also be positive in the second quadrant. So to find this reference angle, π - 0.61

𝜃 = 2.53