Download Trigonometric Functions Center 8: Using Calculators with Trig

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
B) sin 45°
45 stands for an angle measure that is in radians.
Make sure that the calculator is in the radian mode!
45° is an angle measure in degrees. You may use
the degree mode or the degree symbol to evaluate.
sin(45) = 0.851
sin(45°) = 0.707
Try: Evaluate.
1. cos 3
4. tan 135°
2. tan 5°
3. sin π
 9 
5. sin  

 8 
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.
csc  
1
sin 
sec  
1
cos 
cot  
1
tan 
 You MUST use these relationships when using your calculator to evaluate trig functions.
Example: Evaluate.
C) sec 10
D) cot 355°
1.
Make sure your calculator is in the radian mode.
2.
Remember that
3.
Type the expression in terms of cosine.
sec(10) =
sec(10) = 1/cos(10) = -1.192
1
.
cos(10)
1.
Make sure your calculator is in the degree mode.
2.
Remember that
3.
Type the expression in terms of tangent.
cot(355°) =
1
.
tan( 355 )
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

14
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: “All students take calculus,” to remember
the quadrants in which the three main trig functions
are positive.
Students –
ALL – all trig
Sine & cosecant
are positive in Q2
functions are
positive in Q1
Take – Tangent
Calculus –
& cotangent are
positive in Q3
Cosine & secant
are positive in Q4
Find θ for the following conditions. Round your answer to the tenths place for degrees.
Example:
Try:
E) cos θ = -0.389 when 0 < θ < 360°
13. tan θ = 12.052 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°
Solutions are in _______ or _______.
Use the __________ mode.
Type: ____________