Trigonometric Ratios of Some Specific Angles

Trignometric table

0^\circ 30^\circ 45^\circ 60^\circ 90^\circ
Sin \theta 0 \dfrac{1}{2} \dfrac{1}{{\sqrt 2 }} \dfrac{{\sqrt 3 }}{2} 1
Cos \theta 1 \dfrac{{\sqrt 3 }}{2} \dfrac{1}{{\sqrt 2 }} \dfrac{1}{2} 0
Tan \theta 0 \dfrac{1}{{\sqrt 3 }} 1 \sqrt 3 Not defined
Cosec \theta Not defined 2 \sqrt 2 \dfrac{2}{{\sqrt 3 }} 1
Sec \theta 1 \dfrac{2}{{\sqrt 3 }} \sqrt 2 2 Not defined
Cot \theta Not defined \sqrt 3 1 \dfrac{1}{{\sqrt 3 }} 0

Example

Find the lengths of the sides BC and AC in triangle ABC, right-angled at B where AB = 25 cm and \angle ACB = 30^\circ using trigonometric ratios.

tan C = \dfrac{{AB}}{{BC}}

tan 30^\circ

\dfrac{{25}}{{BC}} = \dfrac{1}{{\sqrt 3 }}

BC =25\sqrt 3 cm

sin 30^\circ =\dfrac{{AB}}{{AC}}

\dfrac{1}{2} = \dfrac{{25}}{{AC}}

AC = 50 cm

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