Trigonometric Ratios of Some Specific Angles

Mathematics Class X Introduction to Trigonometry Trigonometric Ratios of Some Specific Angles

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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