Question

find the other five trigonometric ratio if sin A =√3/2

Answer 1

sin A = root 3/2

opposite side / hypotenus = root 3/2

opposite side = root 3

hypotenus = 2

so

as we know that.

( hypotenus )^2 = ( opposite side )^2 + ( adjacent side )^3

2^2 = root 3 ^2 + ( adjecent side )^2

4 - 3 = adjecent side ^2

adjacent sides = 1

so cos A = adjacent side / hypotenus

= 1/2

tan A = opposite side / adjecent side

= root3 /2

cosec A = 1/ sin A

= 1/ root3/2

= 2/ root 3

sec A = 1/cos A

= 1/ 1/2

= 2

cot A = 1/ tan A

= 1/ root3/1

= 1/root 3

Answer 2

if, sin A=√3/2
then cosec A=2/√3,
and sin²A+cos²A=1,
so, (√3/2)²+cos²A=1
=cos²A= 1-3/4
=cos²A= 1/4
=cos A= 1/2,
then, sec A= 2
now, tan A=sin A/cosA
so tan A= √3/2÷1/2
             =√3/2*2/1
             =√3,
and ∴cot A= 1/√3