Trigonometric Ratios For 30 Degrees: Value for the Trigonometrical Ratios for certain angle such as $30^0$ , $60^0$ , $90^0$ and $45^0$ are commonly called standard angles and the trigonometrical ratios of these angles are frequently used to solve particular angles. In this section we will derive the value of trigonometric ratios for $30^0$ .

we have

$sin ; 30^o=frac {1}{2}$ $cos ; 30^o=frac {sqrt {3}}{2}$ $tan ; 30^o=frac {1}{sqrt {3}}$

$cosec ; 30^o=frac {1}{sin ; 30^o}=2$ $sec ; 30^o=frac {1}{cos ; 30^o}=frac {2}{sqrt {3}}$ $cot ; 30^o=frac {1}{tan ; 30^o}=sqrt {3}$

$large angle A$	sin A	cos A	tan A	cosec A	sec A	cot A
$large 30^{circ}$	$large frac{1}{2}$	$large frac{sqrt{3}}{2}$	$large frac{1}{sqrt{3}}$	2	$large frac{2}{sqrt{3}}$	$large sqrt{3}$

Illustration: Simplify the given expression $sin ;30^0 cos ;30^0;(1+ tan; 30^0)$

Solution: To solve this expression we will substitute the value of the ratios at $30^0$

$sin ;30^0 cos ;30^0;(1+ tan; 30^0)$

$=frac{1}{2}times frac{sqrt3}{2};(1+frac{1}{sqrt3})$

$=frac{sqrt3}{4};times;(frac{sqrt3+1}{sqrt3})$

$=frac{sqrt3+1}{4}$

Sample Questions

(More Questions for each concept available in Login)

Question : 1

The value for the following expression is ____________. $frac{6;sin 30^0-2sqrt3;cos 30^0}{6;sin 30^0 +2sqrt3;cos30^0}$
A. -3	B. 3	C. 0	D. 6
Right Option : C
View Explanation

Question : 2

The value for the expression is ____________. $frac{sqrt{13};sin 30^0+2;cos 30^0}{sqrt{13};sin 30^0 -2;cos30^0}$
A. $sqrt{13}-2sqrt3$ $sqrt{13}-2sqrt3$	B. $sqrt{13}+2sqrt3$	C. $(sqrt{13}-2sqrt3)^2$	D. $(sqrt{13}+2sqrt3)^2$
Right Option : D
View Explanation

Question : 3

sin 2A = 2 sin A is true when A =
A. $0^o$	B. $30^o$	C. $45^o$	D. $60^o$
Right Option : A
View Explanation

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Trigonometric ratios for 30 degrees

Trigonometric ratios for 30 degrees

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