Question

यदि sin@=4/5 हो तो cos@, tan@ का मान ज्ञात कीजिए। ​

Answer 1

imagine you have triangle ABC , see figure in attachment

Given :- sin@=4/5

so sin@= perpendicular/hypotenuse

perpendicular=4

hypotenuse=5

we need to find base =??

okay , so we use Pythagoras theorem

${ac}^{2} = {bc}^{2} + {ac}^{ 2} \\ {4}^{2} = {5}^{2} + {ac}^{2} \\ {ac}^{2} = {5}^{2} - {4}^{2} \\ {ac}^{2} = 25 - 16 \\ {ac}^{2} = 9 \\ ac = \sqrt{9} \\ ac = 3$

so now we find base = 3

cos@=[tex]\frac{base}{hypotenuse}[/tex]

cos@=$\frac{</u></strong><strong><u>3</u></strong><strong><u>}</u></strong><strong><u>{</u></strong><strong><u>5</u></strong><strong><u>}$

tan@=$\frac{</u></strong><strong><u>sin@</u></strong><strong><u>}{</u></strong><strong><u>c</u></strong><strong><u>os@</u></strong><strong><u>}$

tan@= $\frac{</u></strong><strong><u>4</u></strong><strong><u>\</u></strong><strong><u>t</u></strong><strong><u>i</u></strong><strong><u>m</u></strong><strong><u>e</u></strong><strong><u>s</u></strong><strong><u>5</u></strong><strong><u>}{</u></strong><strong><u>5</u></strong><strong><u>\</u></strong><strong><u>t</u></strong><strong><u>i</u></strong><strong><u>m</u></strong><strong><u>e</u></strong><strong><u>s</u></strong><strong><u>3</u></strong><strong><u>}$

tan@= $\frac{</u></strong><strong><u>2</u></strong><strong><u>0</u></strong><strong><u>}{</u></strong><strong><u>1</u></strong><strong><u>5</u></strong><strong><u>}$

Hence, Cos@=3/5

tan@= 20/15. or

tan@= 4/3

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