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Basic Trigonometric Ratios

Exact values of the trigonometric ratios

  • For the angles \(30^{\circ}\), \(45^{\circ}\) and \(60^{\circ}\) we can find the exact values for the trigonometric ratios.
  • These ratios are given in the Table below:

 

\(\theta\) \(30^{\circ}\) \(45^{\circ}\) \(60^{\circ}\)
\(
\sin\theta
\)
\(
\frac{1}{2}
\)
\(
\frac{1}{\sqrt{2}}
\)
\(
\frac{\sqrt{3}}{2}
\)
\(
\cos\theta
\)
\(
\frac{\sqrt{3}}{2}
\)
\(
\frac{1}{\sqrt{2}}
\)
\(
\frac{1}{2}
\)
\(
\tan\theta
\)
\(
\frac{1}{\sqrt{3}}
\)
\(
1
\)
\(
\sqrt{3}
\)

Using these triangles assists in remembering these ratios.