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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

5.
Given $space secθ space equals space 13 over 12 comma space$ calculate all other trigonometric ratios.

Let us draw a right angle triangle, right angled at B.
We know that:

secθ space equals space 13 over 12 equals AC over AB

Let AB = 12 K, AC = 13K
where K is a positive number.
Let us draw a right angle triangle, right angled at B.We know that:

Using Pythagoras theorem, we have
AC² = AB² + BC²⇒(13 K)² = (12 K)² + BC²⇒169 K² = 144 K² + BC²⇒BC² = 169 K²-144 K²BC² = 25 K² $rightwards double arrow$ BC = 5 K.
Now,
Let us draw a right angle triangle, right angled at B.We know that:

and $cosecθ space equals space AC over BC equals fraction numerator 13 straight K over denominator 5 straight K end fraction equals 13 over 5.$

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