Exact Values of Trigonometric Ratios for 30°, 45°, and 60°
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Exact Values of Trigonometric Ratios for 30°, 45°, and 60°
The special right triangles can be used to determine the exact values of the trigonometric ratios for angles of \(30^\circ\), \(45^\circ\), and \(60^\circ\).
The exact values of sin \(\theta\), cos \(\theta\), and tan \(\theta\) for an angle \(\theta\), where \(\theta\) is \(30^\circ\), \(45^\circ\), and \(60^\circ\), are summarized in the table.
| \(\theta\) | sin \(\theta\) | cos \(\theta\) | tan \(\theta\) |
| \[30^\circ\] | \[\frac{1}{2}\] | \[\frac{\sqrt{3}}{2}\] | \[\frac{\sqrt{3}}{3}\] |
| \[45^\circ\] | \[\frac{\sqrt{2}}{2}\] | \[\frac{\sqrt{2}}{2}\] | \[1\] |
| \[60^\circ\] | \[\frac{\sqrt{3}}{2}\] | \[\frac{1}{2}\] | \[\sqrt{3}\] |