In ΔABC, right angled at B. AB = 24 cm, BC = 7 cm. Determine:(i

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Introduction to Trigonometry

Long Answer Type

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1. In ΔABC, right angled at B. AB = 24 cm, BC = 7 cm. Determine:
(i) sin A cos A,
(ii) sin C, cos C.

Let AB = 24 cm
BC = 7cm Using Pythagoras theorem, we have
AC² = AB² + BC²= (24 cm)²+ (7 cm)²= 576 cm² + 49 cm²= 625 cm²So, AC = 25 cm
Let AB = 24 cmBC = 7cm Using Pythagoras theorem, we haveAC2 = AB2 +
Now,

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2. In the given figure, find tan P - cot R.

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Short Answer Type

3.

If $sinA space equals space 3 over 4 comma space$ 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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Long Answer Type

5.

Given $space secθ space equals space 13 over 12 comma space$ 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 = $7 over 8 comma$ evaluate:
$fraction numerator left parenthesis 1 plus sinθ right parenthesis space left parenthesis 1 minus sinθ right parenthesis over denominator left parenthesis 1 plus cosθ right parenthesis space left parenthesis 1 minus cosθ right parenthesis end fraction$

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Short Answer Type

8. If 3 cot A = 4, check whether

fraction numerator 1 minus tan squared straight A over denominator 1 plus tan squared straight A end fraction equals cos squared straight A space minus space sin squared straight A

or not.

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Long Answer Type

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

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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 ΔPQR, 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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