Question

If A is an acute angle and tan A = find all the trigonometric ratios of A​

Answer 1

Answer:

Step-by-step explanation:

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

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

Given tan A =$\frac{12}{5}$

cot A = $\frac{5}{12}$

$sec^{2}A=1+tan^{2}A$

$=1+(\frac{12}{5})^{2} \\=1+\frac{144}{25}\\=\frac{25+144}{25} \\=\frac{169}{25} \\=>sec^{2}=\frac{169}{25} \\sec=\frac{13}{5} \\cosA=\frac{1}{secA}=\frac{5}{13}\\tanA=\frac{sinA}{cosA}\\ sinA=cosA*tanA\\\frac{5}{13} \frac{12}{5}\\\frac{12}{13}\\\\cosecA=\frac{1}{sinA}=\frac{13}{12}$