Trigonometric Ratios for 45 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 $45^0$ .

$large angle A$	sin A	cos A	tan A	cosec A	sec A	cot A
$large 45^{circ}$	$large frac{1}{sqrt{2}}$	$large frac{1}{sqrt{2}}$	1	$large {sqrt{2}}$	$large {sqrt{2}}$	$large 1$

Illustration: Simplify the given expression $sin ;45^0 + cos ;45^0;(1+ sin; 45^0;cos;45^0)$

Solution: To solve this expression we will substitute the value of the ratios at $45^0$

$sin ;45^0 + cos ;45^0;(1+ sin; 45^0;cos;45^0)$

$=frac{1}{sqrt 2}+frac{1}{sqrt 2}(1+frac{1}{sqrt 2}times frac{1}{sqrt2})$

$=frac{1}{sqrt 2}+frac{1}{sqrt 2}(1+frac{1}{2})$

$=frac{1}{sqrt 2}+frac{1}{sqrt 2}times frac{3}{2}$

$=frac{1}{sqrt 2}times (1+ frac{3}{2})$

$=frac{1}{sqrt 2}times frac{5}{2}$

$=frac{5}{2sqrt 2}$

Sample Questions

(More Questions for each concept available in Login)

Question : 1

For an actue $Theta ,sin: : Theta +cos: : Theta$ takes the greatest value when $Theta$ is
A. $30^o$	B. $45^o$	C. $60^o$	D. $90^o$
Right Option : B
View Explanation

Question : 2

Solve the following Expression : $5Sin^245^0+Cos^245^0-4Tan^245^0$
A. -1	B. 8	C. 3	D. 1
Right Option : A
View Explanation

Question : 3

Find the value of 'a' if $frac {a;sin^2;30^o;cos^2;60^o}{4;cos^2;45^o}=frac {3;sin^2;45^o+2;cos^2;30^o}{sin^290^o-4;cos^2;45^o}$
A. - 48	B. - 90	C. - 96	D. - 95
Right Option : C
View Explanation

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Trigonometric ratios for 45 degrees

Trigonometric ratios for 45 degrees

Students / Parents Reviews [10]

Aman Kumar Shrivastava

Archit Segal

Shreya Shrivastava

Cheshta

Barkha Arora

Om Umang

Hiya Gupta

Yatharthi Sharma

Shivam Rana

Manish Kumar