Trigonometric Ratios


 
 
Concept Explanation
 

Trigonometric Ratios

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}

Right Option : A
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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

Right Option : D
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Explanation
Question : 3

Find the value of 2;tan;theta when it is given that

sin; theta = frac{3}{5}

Right Option : B
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Explanation
 
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