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Introduction to Trigonometry

Long Answer Type

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

Let
PQ = 12K
and
PR = 13K
Using Pythagoras theorem, we have
PR² = PQ² + QR²⇒(13K)² = (12K)² + QR²⇒169K² = 144K² + QR²⇒QR² = 169K² - 144K²⇒QR² = 25K²So, QR = 5K
LetPQ = 12KandPR = 13KUsing Pythagoras theorem, we havePR2 = PQ2 +
Now,
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Therefore,
$tanP minus cotR space equals space 5 over 12 minus 5 over 12 equals 0.$

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Short Answer Type

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

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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If cot θ = $7 over 8 comma$ evaluate:
$fraction numerator left parenthesis 1 plus sinθ right parenthesis space left parenthesis 1 minus sinθ right parenthesis over denominator left parenthesis 1 plus cosθ right parenthesis space left parenthesis 1 minus cosθ right parenthesis end fraction$