Question

Given sina =3/5 find the other trigonometric ratios of the angle a

Answer 1

cos A=4/5
tan A=3/4
cosec A=5/3
sec A=5/4
cot A=4/3

Answer 2

"Trigonometric ratios of the angle 'a' is

$\sin A=\frac{3}{5}$

$\cos A=\frac{4}{5}$

$\tan A=\frac{3}{4}$

$\csc A=\frac{5}{3}$

$\sec A=\frac{5}{4}$

$\cot A=\frac{4}{3}$

Given:

$\sin A=\frac{3}{5}$

X = 5

P = 3

B = ?

To find:

Trigonometric ratios of angle a

Solution:

Pythagoras theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

According to Pythagoras theorem,

$P^{2}+B^{2}=X^{2}$

Substituting, $B^{2}+3^{2}=5^{2}$

$B^{2}=5^{2}-3^{2}$

$25-9=16=B^{2}$

B=4

$\sin A=\frac{\text {Opposite side}}{\text {Hypotenuse}}=\frac{3}{5}$

$\cos A=\frac{\text {Adjecent side}}{\text {Hypotenuse}}=\frac{4}{5}$

$\tan A=\frac{\text {Opposite side}}{\text {Adjecent side}}=\frac{3}{4}$

$\csc A=\frac{1}{\sin A}=\frac{5}{3}$

$\sec A=\frac{1}{\cos A}=\frac{5}{4}$

$\cot A=\frac{1}{\tan A}=\frac{4}{3}$"