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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.

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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:
$fraction numerator left parenthesis 1 plus sinθ right parenthesis space left parenthesis 1 minus sinθ right parenthesis over denominator left parenthesis 1 plus cosθ right parenthesis space left parenthesis 1 minus cosθ right parenthesis end fraction$

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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.

We have,
Let
PR + QR = 25 cm ..(i)
PR = x cm
QR = (25 - x) cm.
Using Pythagoras theorem, we have
PR² = PQ² + RQ²⇒x² = (5Y + (25 - x)²x² = 25 + 625 + x² - 50x
⇒50x = 650
⇒x = 13 cm
We have,LetPR + QR = 25 cm ..(i)PR = x cmQR = (25 - x) cm.Using Py

Now,
PR = x = 13 cm QR = (25 - x) = 12 cm
and
PQ = 5 cm
Now,
PQ = 5 cm
$sin space straight P space equals space RQ over PR space equals space 12 over 13. CosP space equals space PQ over PR space equals space 5 over 13.$
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