Question

Determine the value of θ to the nearest degree if 90 degrees ≤ θ ≤ 180 degrees for cot θ = -0.2679.

Answer 1

Using the calculator we find that

`\cot ^(-1)(-0.2679)=-75^o`

The angle here is given is measured in the clockwise direction. If we convert it into the anti-clockwise direction, the angle will become 360 - 75 = 285 degrees. This angle lies in the fourth quadrant.

Since it is given that theta lies in the second quadrant. Subtract 180 from 285 to find the angle that has the same value as 285.

The angle in the second quadrant is 285 - 180 = 105 degrees.

Thus, the value of theta is 105 degrees.