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Trigonometric ratios for 45 degrees

Introduction to Trigonometry - Concepts

Identifying Hypotenuses In A Right Triangle

Identifying Adjacent Side To An Angle

Identifying Opposite Side To An Angle

Trigonometric Ratios

Reciprocal Trigonometric Ratios

Trigonometric ratios for 30 degrees

Trigonometric ratios for 60 degrees

Trigonometric ratios for 45 degrees

Trigonometric ratios for 90 degrees

Class - 9th IMO Subjects

Concept Explanation

Trigonometric ratios for 45 degrees

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

Simplify the given expression: $Sin45^0Cos45^0+tan45^0sin45^0$
A. $frac{1}{2}+frac{2}{sqrt2}$	B. $frac{4}{3}+frac{1}{sqrt2}$	C. $frac{1}{2}+frac{1}{sqrt2}$	D. $frac{1}{2}+frac{3}{sqrt2}$
Right Option : C
View Explanation

Question : 2

$frac {1-tan^245^o}{1+tan^245^o}is : : equal : : to$
A. $tan : 90^o$	B. $1$	C. $sin: : 45^o$	D. $sin: : 0^o$
Right Option : D
View Explanation

Question : 3

Solve the given expression : $sin;45^0+cos;45^0+(2+tan ;45^0+cot;45^0)$
A. $frac{5sqrt2+8}{2}$	B. $frac{2sqrt2+5}{2}$	C. $frac{2sqrt3+8}{3}$	D. $frac{2sqrt2+8}{2}$
Right Option : D
View Explanation

Chapters

Polynomials II

Direct and Inverse Variation

Linear Equations in One Variable

Introduction to Trigonometry

Introduction to Euclids Geometry

Herons Formula Complete

Polynomial I

Surface Area and Volume II

Surface Area and Volume I

Coordinate Geometry

Constructions

Areas Of Parallelograms And Triangles II

Areas Of Parallelograms And Triangles I

Linear Equations in Two Variables

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Trigonometric ratios for 45 degrees

Trigonometric ratios for 45 degrees

Students / Parents Reviews [10]

Shreya Shrivastava

Archit Segal

Hiya Gupta

Shivam Rana

Prisha Gupta

Aman Kumar Shrivastava

Om Umang

Ayan Ghosh

Eshan Arora

Yatharthi Sharma