C. Special Right Triangles
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C. Special Right Triangles
When you are asked to provide an
exact value
for an answer to a mathematical problem, it means your answer cannot be an approximated decimal value, so avoid your calculator! An exact value is a mathematical expression, in simplified form, that can involve symbols, fractions, and radicals. In trigonometry, you will be asked to provide the exact values of trigonometric ratios. Examples of exact values and their decimal approximations are provided in the table.
Special Right Triangles
Two special right triangles can be used to determine the exact values of the primary trigonometric ratios for the angles \(30^\circ\), \(45^\circ\), and \(60^\circ\).
| Exact Value | Decimal Approximation
(rounded to the nearest thousandth) |
|
\(2\pi \)
|
\(6.283\)
|
| \[\frac{2}{7}\] |
\(0.286\)
|
| \[\frac{\sqrt{2}}{2}\] |
\(0.707\)
|
Special Right Triangles
Two special right triangles can be used to determine the exact values of the primary trigonometric ratios for the angles \(30^\circ\), \(45^\circ\), and \(60^\circ\).