Question

in∆ABC , angle B=90°. If sec0=13/12, calculate all other trigonometric ratios​

Answer 1

Answer:

Step-by-step explanation:

tan∅ = 5 /12

sin∅ = 5/13

cos∅ = 12/13

cosec∅ = 13/5

Answer 2

Given that,

$\qquad \rm { • sec \: θ = \dfrac{13}{12} }$

__________

We have to find,

$\qquad \rm { • All \: trigonometric \: ratios }$

__________

Solution,

We know that ,

$\qquad \rm { • sec \: θ = \dfrac{Hypotenuse}{Base} }$

So,

$\qquad \rm { • Hypotenuse = 13}$

$\qquad \rm { • Base = 12}$

___________

Applying pythagoras property-

$\rm\red { {H}^{2} = {B}^{2} +{P}^{2} }$

$\rm { {P}^{2} = {H}^{2} - {B}^{2} }$

$\rm { \implies {P}^{2} = {H}^{2} - {B}^{2} }$

$\rm { \implies {P}^{2} = {13}^{2} - {12}^{2} }$

$\rm { \implies {P}^{2} = 169 - 144 }$

$\rm { \implies {P}^{2} = 25 }$

$\rm { \implies P = \sqrt{25}= 5 }$

____________

$\qquad \rm { • Hypotenuse = 13}$

$\qquad \rm { • Base = 12}$

$\qquad \rm { • Perpendicular = 5}$

____________

$\qquad \rm { • sin \:θ = \dfrac{P}{H} = \dfrac{5}{13} }$

$\:$

$\qquad \rm { • cos \:θ = \dfrac{B}{H} = \dfrac{12}{13} }$

$\:$

$\qquad \rm { • tan \:θ = \dfrac{P}{B} = \dfrac{5}{12} }$

$\:$

$\qquad \rm { • cosec \:θ = \dfrac{H}{P} = \dfrac{13}{5} }$

$\:$

$\qquad \rm { • sec \:θ = \dfrac{H}{B} = \dfrac{13}{12} }$

$\:$

$\qquad \rm { • cot \:θ = \dfrac{B}{P }= \dfrac{12}{5} }$