Trigonometry ratio. Find the values of theater between 0° and 360°which satisfy each of the following . A.sin theater= 0.4396 B.cos theater=0.8427 C.tan theater= -2.4398 D.tan theater= 0.4926

Answer 1

A. sin θ = 0.4396

Using a calculator, we can find that the inverse sine of 0.4396 is approximately 25.98 degrees. However, sine is positive in both the first and second quadrants, so we also need to find the reference angle in the second quadrant which is 180 - 25.98 ≈ 154.02 degrees. Therefore, the solutions are θ ≈ 25.98 degrees and θ ≈ 154.02 degrees.

B. cos θ = 0.8427

Using a calculator, we can find that the inverse cosine of 0.8427 is approximately 31.94 degrees. However, cosine is positive in both the first and fourth quadrants, so we also need to find the reference angle in the fourth quadrant which is 360 - 31.94 ≈ 328.06 degrees. Therefore, the solutions are θ ≈ 31.94 degrees and θ ≈ 328.06 degrees.

C. tan θ = -2.4398

Using a calculator, we can find that the inverse tangent of -2.4398 is approximately -67.98 degrees. However, tangent is negative in the second and fourth quadrants, so we also need to add 180 degrees to get the solution in the second quadrant which is 180 - 67.98 ≈ 112.02 degrees. Also, we need to add 360 degrees to get the solution in the fourth quadrant which is 360 - 67.98 ≈ 292.02 degrees. Therefore, the solutions are θ ≈ 112.02 degrees and θ ≈ 292.02 degrees.

D. tan θ = 0.4926

Using a calculator, we can find that the inverse tangent of 0.4926 is approximately 25.87 degrees. However, tangent is positive in the first and third quadrants, so we also need to add 180 degrees to get the solution in the third quadrant which is 180 + 25.87 ≈ 205.87 degrees. Therefore, the solutions are θ ≈ 25.87 degrees and θ ≈ 205.87 degrees.