What are the solutions to `sin(theta) = -0.4321` ?

For sin(θ) = -0.4321, 0 ≤ θ ≤ 360°

  1. How many solutions are possible?
  2. In which quadrants would you find the solutions?
  3. Determine the reference angle for this equation to the nearest degree.
  4. Determine all the solutions to the equation to the nearest degree.




Expert Answers

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Draw the graph and a line at `y=-0.4321`

The line cuts the graph twice in the range, so there are two solutions.

The solutions are in the bottom right quadrant.

The reference angle is the solution in the range `-90 <theta < 90`

and is the solution to `sin^(-1)(-0.4321) = -26 ^@`

The solutions are of the form `180n - 26`,`n` even and `180n +26``n`odd

ie,  `theta =` `-386^@, -154^@, -26^@, 206^@, 334^@`  etc

There are two solution in 0<theta<360

The solutions are in the bottom right quadrant

The reference angle is in the range [-90,90] and is -26 degrees

theta = -386, -154, -26, 206, 334 etc

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