If sin θ = √3/2, find the value of all T-ratios of θ.

Dear Student

Given function: sin θ = √3/2
We know that sin𝜃= BC/AC = (Perpendicular)/Hypotenuse =√3/2
By Pythagoras Theorem:
AC^2 = AB^2 + BC^2
AB^2 = AC^2 - BC^2
= 4k^2–3k^2
= k^2

AB = k

Find other T-ratios using their definitions:

Cos 𝜃= AB/AC = 1/2
Tan𝜃= BC/𝐴𝐵= √3
𝑐𝑜𝑠𝑒𝑐 𝜃= 1/sin𝜃= 2/√3
sec𝜃= 1/cos𝜃= 2
cot𝜃= 1/tan𝜃= 1/√3

Thanks