Determine the approximate value of each trigonometric ratio. Justify the sign for each ratio.

Question

1.cos 2.51

2.csc (-125°)

Answer 1

Sal,

 

You will need a calculator for these questions.

 

For 1, the calculator must be set to radian mode. Since I do not know what kind of calculator you are using, I can only tell you the answer is -0.8071 (rounded to 4 decimal places).

 

For 2, the calculator must be set to degree mode. Most calculators do not have a csc function, so you must find it using 1/sin(-125°) = -1.2208 (again rounded to 4 decimal places).

 

To justify the signs, remember the quadrant for each angle. 2.51 radians is larger than π/2 and smaller than π, so the angle lies in Quadrant II, where cosine is negative. -125° lies in Quadrant III, so the sine is negative, and so is the cosecant.

 

If my explanation is not what you wanted, please reply with any questions.