INTRODUCTION TO TRIGONOMETRY
EXERCISE 8.1
1. In `∆ ABC`, right-angled at `B, AB = 24 cm, BC = 7 cm.` Determine :
`(i) sin A, cos A (ii) sin C, cos C`
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2. In Fig. find `tan P – cot R`.
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3. If `sin A =
3/4` calculate `cos A` and `tan A`.
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4. Given `15 cot A = 8`, find `sin A` and `sec A`.
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5. Given `sec θ =
13/12` calculate all other trigonometric ratios.
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6. If `∠ A` and `∠ B` are acute angles such that `cos A = cos B`, then show that `∠ A = ∠ B`.
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7. If `cot θ =
7/8` evaluate:
(i) `\frac{(1 + \sin \theta) (1 - \sin \theta)}{(1 + \cos \theta) (1 - \cos \theta)}`
(ii) `\cot^2 \theta`
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9. In `\Delta ABC`, right-angled at B, if `tan A =
1/sqrt 3` find the value of:
(i) `\sin A \cos C + \cos A \sin C`
ii) `\cos A \cos C – \sin A \sin C`
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10. In `∆ PQR`, right-angled at `Q, PR + QR = 25 cm` and `PQ = 5 cm`. Determine the values of
sin P, cos P and tan P.
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11. State whether the following are true or false. Justify your answer.
(i) The value of tan A is always less than 1.
(ii) `sec A =
12/5` for some value of angle A
(iii) cos A is the abbreviation used for the cosecant of angle A.
(iv) cot A is the product of cot and A.
(v) `sin θ =
4/3` for some angle θ.
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EXERCISE 8.2
1. Evaluate the following :
(i) sin 60° cos 30° + sin 30° cos 60°
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(ii) `2 tan^2
45° + cos^2
30° – sin^2
60°`
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(iii) `\frac {cos 45°}{ sec 30° + cosec 30°}`
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(iv) `\frac{sin 30° + tan 45° – cosec 60°}{sec 30° + cos 60° + cot 45°
}`
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(v) `\frac{5 cos^2 60° + 4 sec^2 30° - tan^2 45°}{sin^2 30° + cos^2 30°}`
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2 (i) `\frac{2 tan 30°}{1 + tan^2 30°}`
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(ii) `\frac{1 - tan^2 45°}{1 + tan^2 45°}`
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(iii) ` sin 2A = 2 sin A` is true when A =
(A) 0° (B) 30° (C) 45° (D) 60°
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(iv) `\frac{2 tan 30°} {1 - tan^2 30°}`
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