Trigonometric Functions Center 6: Using Calculators with Trig

Sine, Cosine, & Tangent

Your calculator uses three of the six trigonometric function, sine (sin), cosine (cos), and tangent (tan). Evaluating these three functions for different angles is easy; just type in the original problem, and press “ENTER.”

Be aware that there are two modes on your calculator for angle values, degrees and radians; so, you should check the MODE button before doing calculations!

Example: Evaluate.

A) sin 45
45 stands for an angle measure that is in radians. Make sure that the calculator is in the radian mode!
sin(45) = 0.851 / B) sin 45°
45° is an angle measure in degrees. You may use the degree mode or the degree symbol to evaluate.
sin(45°) = 0.707

Try: Evaluate.

1. cos 3 / 2. tan 5° / 3. sin π
4. tan 135° / 5. sin / 6. cos π°

Cosecant, Secant & Cotangent

Your calculator does not have a cosecant, secant, or cotangent button, so you need to remember that they are reciprocal functions of sine, cosine, and tangent respectively.

 You MUST use these relationships when using your calculator to evaluate trig functions.

Example: Evaluate.

C) sec 10
  1. Make sure your calculator is in the radian mode.
  2. Remember that sec(10) = .
  3. Type the expression in terms of cosine.
sec(10) = 1/cos(10) = -1.192 / D) cot 355°
  1. Make sure your calculator is in the degree mode.
  2. Remember that cot(355°) = .
  3. Type the expression in terms of tangent.
cot(355°) = 1/ tan(355°) = -11.430

Try: Evaluate.

7. cot 451° / 8. csc 238° / 9. sec 8°
10. csc π / 11. sec 8 / 12. cot

Finding Angles: 0 θ < 360° or 0 θ < 2π

  • In one rotation, there are usually two angles that would be possible solutions.
  • Your calculator will give you only one solution.
  • Draw a picture so that you’ll remember in which quadrants the angles will be.
  • Check the mode on your calculator! Use sin-1, cos-1, or tan-1 to get the angle.
  • Use the idea of reference angles to find the “missing” angle from your picture.

Learn: “Allstudents take calculus,” to remember the quadrants in which the three main trig functions are positive.

Find θ for the following conditions. Round your answer to the tenths place for degrees.

Example:
E) cos θ = -0.389 when 0 θ < 360°

Solutions are in Q2 or Q3.
Use the degree mode.
Type: cos-1(-0.389)
cos-1(-0.389) = 112.8
The calculator gave and answer of 112.8°, which is a Q2 angle. We need to find the other angle (which is in Q3 for this problem.)
1. Find the reference angle. (180 – 112.8 = 67.2)
2. Use the reference angle to find the other possibility for θ. (In this case, add it to 180.)
180 + 67.2 = 247.2
The Q2 angle is 112.8°, and the Q3 angle is 247.2° / Try:
13. tan θ = 12.052 when 0 θ < 360°
Solutions are in ______or ______.
Use the ______mode.
Type: ______