MATH122
Degrees or Radians?

Now that we know about two different measures for angles, there is the problem of recognizing which one we are using.

Rule: If there is no symbol on the angle, it is measured in radians. A degree symbol is necessary for an angle measured in degrees.

Thus:

sin 30 is the sine of 30 radians or about -0.9980

while

sin 30° is the sine of 30 degrees or exactly 0.5.

and

tan (π/4) is the tangent of π/4 radians or exactly 1,
sec 5 is the secant of 5 radians or about 3.5253,
sec 5° is the secant of 5 degrees or about 1.0038.

This seems really simple and it is, but our calculator MUST be set for the appropriate mode, so

Rule: ALWAYS check the mode setting before using the calculator to evaluate a trig function.

Problems: Evaluate, giving answers with four decimal places of accuracy.

1. sin 30
2. cos (π/5)
3. tan 16°
4. sec 5
5. cot 10°
6. cos (3π/10)

Answers:

1. -0.9880
2. 0.8090
3. 0.2867
4. 3.5253
5. 5.6713
6. 0.5878