Trigonometric ratios for 30 degrees


 
 
Concept Explanation
 

Trigonometric ratios for 30 degrees

Trigonometric Ratios For 30 Degrees: Value for the Trigonometrical Ratios for certain angle such as 30^0,60^090^0 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 Asin Acos Atan Acosec Asec Acot A
large 30^{circ}large frac{1}{2}large frac{sqrt{3}}{2}large frac{1}{sqrt{3}}2large 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
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Question : 1

Solve the following :

frac{5sin30^0-3cos30^0}{5sin30^0+2cos30^0}

 

Right Option : B
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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}

Right Option : D
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Question : 3

The value of the expression 2;cos^2;A -1  when A= 30 is ____________.

 

Right Option : B
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