Topic: Applications of Trigonometric Ratios to Find Unknown Sides of Right-Angled Triangles

Question

Question:

If y is inversely proportional to (tan x)² and y = 2 when x = 30°, find the value of y when this value of x is doubled

Answer 1

y=k/(tanx)^2 = 2= k/(tan30)^2 = k/1/3= 3k

3k=2

k = 2/3

y=(2/3)/(tan60)^2 = (2/3)/3 = 2/9

y = 2/9 when x is doubled from 30 to 60 degrees