Chapter 22. Introduction to Trigonometry NIOS Class 10 Mathematics Chapter-Wise Important Questions and Answers

Chapter 22. INTRODUCTION TO TRIGONOMETRY

Optional Questions and Answers for Algebraic Expressions and Polynomials [1 Mark]

CHECK YOUR PROGRESS 3.1

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Long Questions and Answers for Algebraic Expressions and Polynomials [ 3 or 4 Mark]

CHECK YOUR PROGRESS 22.1

1. In each of the following figures, ΔABC is a right triangle, right angled at B. Find all the trigonometric ratios of θ .

Fig. 22.11

Solution: (i) Here, AB=5 cm , BC=12 cm , AC=13 cm

sinθ=Perpendicularhypotenuse =ABAC=513

cosθ=baseHypotenuse=BCAC=1213

tanθ=Perpendicularbase=ABBC=512

cotθ=baseperpendicular =BCAB=125

secθ=Hypotenusebase=ACBC=1312

cosecθ=Hypotenuseperpendicular =ACAB=135

(ii) Here, AB=3 cm , BC=4 cm and AC=5 cm

sinθ=Perpendicularhypotenuse =ABAC=35

cosθ=baseHypotenuse=BCAC=45

tanθ=Perpendicularbase=ABBC=34

cotθ=baseperpendicular =BCAB=43

secθ=Hypotenusebase=ACBC=54

cosecθ=Hypotenuseperpendicular =ACAB=53

(iii) Here, AB=24 cm , BC=7 cm and AC=25 cm

sinθ=Perpendicularhypotenuse =ABAC=2425

cosθ=baseHypotenuse=BCAC=725

tanθ=Perpendicularbase=ABBC=247

cotθ=baseperpendicular =BCAB=724

secθ=Hypotenusebase=ACBC=257

cosecθ=Hypotenuseperpendicular =ACAB=2524

(iv) Here, AB=6 cm , BC=8 cm and AC=10 cm

sinθ=Perpendicularhypotenuse =BCAC=810=45

cosθ=baseHypotenuse=ABAC=610=35

tanθ=Perpendicularbase=BCAB=86=43

cotθ=baseperpendicular =ABBC=68=34

secθ=Hypotenusebase=ACAB=106=53

cosecθ=Hypotenuseperpendicular =ACBC=108=54

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