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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 45 degrees

Class - 8th Foundation NTSE 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

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

Question : 3

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

Chapters

Exponents and Power II

Prerequiste

Visualising Soild Shapes

Ratio and Proportion

Introduction to Trigonometry

Constructions

Quadrilaterals II

Quadrilaterals I

Linear Equations in One Variable II

Linear Equations in One Variable I

Cube and Cube Roots

Square and Square Root II

Square and Square Root I

Rational Numbers II

Rational Numbers I

Mensuration I

Exponents and Power I

Direct and Inverse Variation II

Direct and Inverse Variation I

Algebraic Expressions

Comparing Quantities III

Comparing Quantities II

Comparing Quantities I

Playing With Numbers

Introduction to Graphs

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Trigonometric ratios for 45 degrees

Trigonometric ratios for 45 degrees

Students / Parents Reviews [10]

Yatharthi Sharma

Cheshta

Hiya Gupta

Archit Segal

Manish Kumar

Aman Kumar Shrivastava

Ayan Ghosh

Shreya Shrivastava

Barkha Arora

Shivam Rana