### More Trig Equations to Solve

Other Resource Pages
Solving Equations Graphically, Solutions to Linear Equations
compute.xls -- Spreadsheet which solves linear and quadratic equations and linear systems
Precalc Notes -- Links to an entire precalc course material
solvtrg.xls -- Spreadsheet which solves triangles by different methods
Intro

To solve an equation means to find all the values that make the statement true.

This might be done graphically, but, most of the time it must be done algebraically.   To solve an equation graphically, draw the graph for each side, member, of the equation and see where the curves cross, are equal. The x values of these points, are the solutions to the equation.

There are many possible outcomes when one solves an equation.
• ONE SOLUTION - the statement is true only once
• MORE THAN ONE SOLUTION - the statement is sometimes true
• EVERY NUMBER IS A SOLUTION - the statement is always true
• THERE IS NO SOLUTION - the statement is false

Consider the following examples.

 1. Solve:   cos( ) = (2)/2, where - < < 2. Solve:   cos( ) = (2)/2, where 0 < < 2       We'll use the same picture and a bit of arithmetic to solve both equations.       The two expressions cos( ) and (2)/2 are equal for 2 values of in the restricted interval between - and . Graphs of the two expressions cross at two values of . When is - /4 and when is /4, the expressions are equal. These are the solutions.       For the interval from 0 to 2 , there are two solutions to cos( ) = (2)/2. One solution is /4. To get the other solution, take - /4 and add 2 . The result is 7 /4. This is the second solution to the equation cos( ) = (2)/2. This solution is readily visible in the next example.
 Solve cos( ) = (2)/2       The two expressions cos( ) and (2)/2 are equal for an infinite number of values of because the cosine function is periodic (infinitly repeating) and the (2)/2 is constant (always the same). Graphs of the two expressions cross an infinite number of times, each equal to 7 /4 ± 2 n and /4 ± 2 n, where n is 0, 1, 2, 3, ... These are the solutions.

Click on the problem to see the solution.
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