TI-92 Algebra Topics:

solve() cSolve() factor() cFactor() expand() tExpand()

tCollect() comDenom() zeros() propFrac() getNum()

The advantage of using the TI-92 calculator is its ability to perform symbolic manipulation of algebraic expressions. This feature, incorporated with the pretty print display, makes the TI-92 a powerful mathematical tool. This tutorial will describe the algebra functions for the TI-92.

solve()

The solve() function can be used to solve a variety of mathematical equations or inequalities. The solve function will return a real solution of an equation. The function csolve() can be used to solve for real or complex solutions. The format of the solve function is

To solve the equation x + 3 = 4 for x, type

in the entry line then press ENTER.

Some of the more commonly used algebra and calculus functions are available through the tab window on the home screen. Pressing F2 (Algebra) then 1: solve( will place the solve function on the entry line.

Note that this technique provides the left parenthesis only. A function will operate on what is enclosed inside the parenthesis.

You can also get to the solve function by pressing the 2nd key then 5 (MATH) then 9: Algebra then 1: Solve.

To solve the equation x² - 1 = 0, type

then press ENTER.

The solve() function can also solve equations symbolically.

The | symbol can be used to restrict the solution. For example, if we only wanted to obtain the positive solution to the problem above enter:

To solve the equation a + b = c for b enter the following:

Use the calculator to solve the quadratic equation ax² + bx + c = 0. Remember to put a multiplication symbol between the variables.

To view the full solution, use the cursor pad to scroll up to the history area and to the right

To solve the inequality 5x - 2 ³ 3 enter the following:

Solve the equation 2^x - 3 = 0

If your calculator is in exact or auto mode you will get the first answer. If the mode is approximate, you will get the second answer. An approximate answer can be obtained in any mode by pressing the diamond key then ENTER.

To solve a trigonometric equation sin(x) = 0 enter the following:

You will get the top answer if the calculator is in degree mode and the bottom answer if in radian mode. The @n1 and @n2 represent integers.

cSolve()

The cSolve() function can be used to find complex solutions to equations. Use the TI-92 to solve the equation

Note that if you tried to solve this equation by using the solve() function instead of csolve(), the result is a false. The function cSolve() will solve equations with real as well as complex solutions.

factor()

The factor() function can be used to find factors of algebraic expressions. To factor the quadratic

enter the following:

The format of the factor function is

Factor 36x²a⁴ - 9 a² for x then for a

The factor function can also be used to factor rational numbers.

cFactor()

The function cfactor() will factor an expression with respect to all of its variables over a common denominator or factor an expression as much as possible towards factors that are linear even if this introduces new non-real numbers.

expand()

The expand() function will expand expressions with respect to its variables. The format of the expand function is

Expand the expressions (x + 2)² and .

Note that the expression (x + 2)² was expanded into a polynomial and the expression was expanded into a partial fraction.

tExpand()

Use the tExpand() function to expand a trigonometric functions. Expand sin(2q)

tCollect()

Use the tCollect() to return an expression in which products and integer powers of sines and cosines are converted to a linear combination of sines and cosines. Expand sin²(2q).

comDenom()

The comDenom() function can be used to reduce expressions to a common denominator.

zeros() and czeros()

The zero() function will return a list of real values that solve the equation

expression = 0. The solution of (x - 2)² + 4 = 0 is an empty set, but the solutions to

(x - 2)² - 4 = 0 are x = 0 and x = 4. The czeros() function will return complex solutions.

The format of the zeros() function is

propFrac()

The propFrac() function will return a rational expression as a sum of and integer and a fraction.

getNum() and getDenom()

The getNum() function transforms an expression into one having a reduced common denominator and then returns the numerator and the getDenom() function does the same thing except returns the common denominator.

Exercises

1.) Solve the equation and get the answer in fractional and

decimal form.

2.) Solve the equation 3y - 2x = 7 for x and y.

3.) Solve .

4.) Solve |x| = 7.

Answers