Question

if A is an acute angle and tanA=12/5 , find all the other trigonometric ratios

Answer 1

Answer:

SinA=P/H=12/13

CosA=B/H=5/13

CosecA=H/P=13/12

SecA=H/B=13/5

Cot A=B/P=5/12

Step-by-step explanation:

Given That Tan A=12/5=P/B

let

$H=\sqrt{12^2+5^2}=\sqrt{144+25}=\sqrt{169}=13\\H=13$

So

the other trigonometric Ratio can be found By using

SinA=P/H=12/13

CosA=B/H=5/13

CosecA=H/P=13/12

SecA=H/B=13/5

Cot A=B/P=5/12

Answer 2

Answer:

Sin A = 12/13

CosA = 5/13

CotA =  5/12

SecA = 13/15

CosecA =  13/12

Step-by-step explanation:

if A is an acute angle and tanA=12/5 , find all the other trigonometric ratios

A is an acute angle so it will be less than 90 deg

Tan A = 12/5

Tan A = Perpendicular / Base

Perpendicular = 12X

12/5 = 12X/Base

=> Base = 5X

Hypotenuse² = Perpendicular²  + Base²

=>   Hypotenuse² = (12X)² + (5X)²

=> Hypotenuse² = 144X² + 25X²

=> Hypotenuse² = 169X²

=> Hypotenuse² = (13X)²

=> Hypotenuse = 13X

Sin A = Perpendicular / Hypotenuse = 12X / 13X = 12/13

CosA = Base / Hypotenuse = 5X / 13X = 5/13

CotA = 1/TanA = 1/(12/5) = 5/12

SecA = 1/CosA = 1/(5/13) = 13/15

CosecA = 1/SinA = 1/(12/13) = 13/12