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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.

938 Views

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.

1135 Views

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.

Let us draw a right triangle right angled at B.
We have,
3 cot A = 4

rightwards double arrow

cotA space equals space 4 over 3 space equals space AB over BC

Let AB = 4K and BC = 3K
Let us draw a right triangle right angled at B.We have,3 cot A = 4

Using Pythagoras theorem, we have
AC² = AB² + BC²= (4K)² + (3K)²= 16K² + 9K² = 25 K²So, AC = 5K
$tan space straight A space equals space BC over AB space equals space fraction numerator 3 straight K over denominator 4 straight K end fraction space equals space 3 over 4$

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and $sinA space equals space BC over AC equals fraction numerator 3 straight K over denominator 5 straight K end fraction space equals space 3 over 5$

L.H.S. = $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$

$space space equals space fraction numerator 1 minus open parentheses begin display style 3 over 4 end style close parentheses squared over denominator 1 plus open parentheses begin display style 3 over 4 end style close parentheses squared end fraction space equals space fraction numerator 1 minus begin display style 9 over 16 end style over denominator 1 plus begin display style 9 over 16 end style end fraction$
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Now,
R.H.S. = $cos squared straight A space minus space sin squared straight A$
$equals space open parentheses 4 over 5 close parentheses squared minus open parentheses 3 over 5 close parentheses squared equals space 16 over 25 minus 9 over 25 space equals space fraction numerator 16 minus 9 over denominator 25 end fraction space equals space 7 over 25$
Hence, L.H.S. = R.H.S.
$or space fraction numerator 1 minus tan squared straight A over denominator 1 plus tan squared straight A end fraction equals cos squared straight A space minus space sin squared straight A.$