Introduction to Algebra using the TI-92 Ó 1997
by Nathan O. Niles
Associate Professor (Retired)
U. S. Naval Academy

14. Trigonometric Functions

The values of the trigonometric functions may be obtained by use of a calculator or from tables. When using a calculator the ‘mode’ must be radians when the argument is an angle in radians or a real number. For an angle measured in degrees the ‘mode’ may be set to degrees or the key combination 2 D may be used.

Example. Find: (a) sin 1. (b) cos(-2.5). (c) tan 7.8. (d) sin 30° . (e) sin 30. (f) tan 45° .
Solution: The following instructions are for the TI-92 Graphing Calculator.

Since there is no ° symbol, the argument is an angle in radians or a real number. The MODE for Angle must be set to ‘Radians’.

(b)   2.5   Displays: -.801144

(c)  7.8   Displays: 18.5068

(d)  30  D   Displays: ½

  displays: .5

(e)  30  Displays: sin(30)

  displays:-.988032

Problem. Find: (a) sin 2. (b) cos(-1.5). (c) tan 8.7. (d) sin 45° . (e) sin 45. (f) tan 60° .

Many of the trigonometric identities can be obtained using the TI-92 Graphing Calculator. We make use of the ‘Algebra Menu’ F2. The results usually are expressed in terms of sines and or cosines.

Example. Find cos (u - v) using the TI-92 Graphing Calculator.

Solution: Turn on the TI-92, clear home screen and entry line:   8 

Display ‘Algebra Menu", select ‘Trig’ and ‘tExpand(’:  9 1

tExpand ( is displayed on the entry line.

Enter the required expression. Be sure to enter the last parentheses ). The left parentheses after tExpand and after  are automatically entered.

u  v   

The display shows: tExpand(cos(u - v))

cos(u)× cos(v) + sin(u)× sin(v)

 Problem. Find sin (u + v) using the TI-92.

Example. Find tan (u + v) on the TI-92.

Solution: Turn on the TI-92, clear home screen and entry line:   8 

Display ‘Algebra Menu", select ‘Trig’ and ‘tExpand(’:  9 1

u  v   

 The display shows: tExpand (tan(u + v))

  Is this expression equivalent to the identity, ?

Divide each term on the right by cos(u) cos(v) to obtain

Simplify to get 

Rewrite to obtain the desired form 

Problem. Find tan (u - v) on the TI-92.

Example. Use the TI-92 to express cos2 u - sin2 u as one term.

Solution: Turn on the TI-92, clear home screen and entry line:   8 

Display ‘Algebra Menu", select ‘Trig’ and ‘tCollect (’:  9 2

tCollect( is displayed on the entry line. Notice the left parentheses is automatically entered. It is also entered automatically when the  and  keys are pressed.

  u    2    u    2  

The display shows: tCollect((cos(u))2 - (sin(u))2) cos(2× u)

 Problem. Use the TI-92 to express 2 sin u cos u as one term.

The TI-92 does not handle all of the composite argument trig identities.
 
 To Table of Contents   To Section 13. Logarithms   To Section 15. Inverse Trig Functions