Trigonometric Ratios

Concept Explanation

Trigonometric Ratios

Let us take a right triangle ABC right angled at B as shown

Here, $large angle CAB$ (or, in brief, angle A ) is an acute angle. Note the position of the side BC with respect to angle A. It faces $large angle A$ . We call it the side opposite to angle A or perpendicular with respect to angle A.. AC is the hypotenuse of the right triangle and the side AB is a part of $large angle A$ , So , we call it the side adjacent to angle A or base with respect to angle A

Note that the position of sides change when you consider angle C in place of A

We now define certain ratios involving the sides of a right triangle, and call them trigonometric ratios.

The trigonometric ratios of the angle A in right triangle ABC are defined as follows:

$sine ;of;angle A=sin;A= frac{side; opposite;to; angle; A }{hypotenuse}=frac{BC}{AC}$

$cosine; of;angle A=cos;A=frac{side;adjacent; to; angle; A}{hypotenuse}=frac{AB}{AC}$

$tangent; of ;angle A=tan;A=frac{side;opposite; to; angle;A }{side;adjacent;to;angle;A}=frac{BC}{AB}$

$tangent; of ;angle A=frac{BC}{AB}=frac{frac{BC}{AC}}{frac{AB}{AC}}= frac{sin;A}{cos ;A}$

Illustration: ABC is a right angled triangle.If AB = 3 cm, BC= 4 cm and CA = 5 cm and $angle;A= theta. ;Find; sintheta.$ .

Solution: In the figure we have a right angled triangle ABC right angled at B and we know that by the definition

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Sample Questions

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Question : 1

Find the value of $sin;theta+ ;2cos;theta$ when it is given that $tan; theta = frac{3}{4}$
A. $dpi{110}frac{11}{5}$	B. $dpi{110}frac{7}{5}$	C. $dpi{110}frac{5}{7}$	D. None of these
Right Option : A
View Explanation

Question : 2

If $sin: : A:cos: : A=4:7,$ then the value of $frac {7: : sin: : A-3: : cos: : A}{7: : sin: : A+2: : cos: : A}$ is
A. $frac{3}{14}$	B. $frac{3}{2}$	C. $frac{1}{3}$	D. $frac{1}{6}$
Right Option : D
View Explanation

Question : 3

Find the value of $2;cos;theta$ When it is given that $tan; theta = frac{a}{b}$
A. $dpi{110}frac{2b}{sqrt{a^2-b^2}}$	B. $dpi{110}frac{2b}{sqrt{a^2+b^2}}$	C. $dpi{110}frac{2a}{sqrt{a^2+b^2}}$	D. None of these
Right Option : B
View Explanation

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Square and Square Root

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Time, Speed and Distance

Partnership and Mixture

Permutation and Combination

Introduction to Trigonometry

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Trigonometric Ratios

Trigonometric Ratios

Trigonometric Ratios

Students / Parents Reviews [10]

Yatharthi Sharma

Manish Kumar

Cheshta

Om Umang

Hiya Gupta

Ayan Ghosh

Aman Kumar Shrivastava

Shivam Rana

Eshan Arora

Prisha Gupta