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Introduction to Trigonometry

Introduction to Trigonometry

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Introduction to Trigonometry

Que. 1. In triangle ABC, right-angled at B, AB = 24 cm and BC = 7 cm. Find the value of the following:

(i) sin A, cos A

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By Pythagoras theorem in triangle ABC,

 K2  =  L2  +  A2

(AC)2 =  (BC)2  +  (AB)2

AC2  =  (7)2  +  (24)2

AC2  =  49  +  576

       AC2  =  625

      AC  =  25 cm

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(ii) sin C, cos C

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Que. 2. In the figure, find the value of tan P – cot R.

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tan P – cot R

By Pythagoras theorem in triangle PQR,

K2  =  A2   +  L2

(PR)2  =  (QR)2  +  (PQ)2

(13)2  =  (QR)2  +  (12)2

169  =  QR2  + 144

169 – 144  = QR2

25  = QR2

QR  =  5 cm.

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Que 3. If sin A = 3/4, calculate the values ​​of cos A and tan A.

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By Pythagoras theorem in triangle ABC,

K2  = A2  +  L2

(AC)2  =  (AB)2  +  (BC)2

(4)2  =  (AB)2  +  (3)2

16 – 9  =  AB2

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Que. 4. If 15 cot A = 8, find the values ​​of sin A and sec A.

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15 cot A  =  8

By Pythagoras theorem in triangle ABC,

K2  = A2  +  L2

(AC)2  =  (AB)2  +  (BC)2

(AC)2  =  (8)2  +  (15)2

AC2  =  64  +  225

AC2  =  289

AC  =  17 cm.

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Que. 5. If

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then calculate all other trigonometric ratios.

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K2  =  A2   +  L2

(PR)2  =  (QR)2  +  (PQ)2

(13)2  =  (12)2  +  (PQ)2

169  =  144  +  PQ2

169 – 144  =  PQ2

PQ2  =  25

PQ  =  5 cm

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Que. 6. If angle A and angle B are acute angles such that cos A = cos B, then show that angle A = angle B.

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AC  =  BC

Angles opposite to equal sides are equal.

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By Pythagoras theorem in triangle ABC

K2  = A2  +  l2

(AC)2  =  (BC)2  +  (AB)2

AC2  =  (7)2  +  (8)2

AC2  =  49  +  64

AC2  =  113

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Que. 8. If 3 cot A = 4, check whether (1 – tan² A) / (1 + tan² A) = cos² A – sin² A or not.

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K2  = A2  +  l2

(AC)2  =  (AB)2  +  (BC)2

AC2  =  (4)2  +  (3)2

AC2  =  16  +  9

AC2  =  25

AC  =  5

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Que. 9. In triangle ABC, right angled at B, if

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So, find the values ​​of the following:

(i) sin A cos C + cos A sin C

(ii) cos A cos C – sin A sin C

By Pythagoras theorem in triangle ABC,

K2  = A2  +  L2

(AC)2  =  (AB)2  +  (BC)2

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AC2  =  3 + 1

AC2  =  4

AC = 2

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1. sin A cos C + cos A sin C

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Que. 10. In triangle PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Find the values ​​of sin P, cos P, and tan P.

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By Pythagoras theorem in triangle PQR,

K2  =  A2   +  L2

(PR)2  =  (QR)2  +  (PQ)2

From equation (1),

(25 – QR)  =  (5)2 + (QR)2

(25)2 – 2 X 25 X QR + (QR)2  =  25 + (QR)2

625 – 50 QR + (QR)2 – 25 + (QR)2  =  0

625 – 50 QR  =  0

– 50 QR  =  – 600

QR  =  12 cm

PR = 25 – QR     =     25 – 12

      = 13 cm

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