Question

If y is inversely proportional to (tan x) and y = 2

when x = 30°, find the value of y when this value
of x is doubled.​

Answer 1

Explanation:

y is inversely proportional to tan x means

`y \ \alpha \ (1)/(tan x)\\\\y = k * (1)/(tanx)`

Given y = 2 when x =30° . So we will find k.

`y =k * (1)/(tanx ) \\\\2 = k * (1)/(tan 30)\\\\k = 2 * tan 30 = 2 * (1)/(√(3)) = (2)/(√(3) )`

Now x is doubled, x = 60°, find y

`y = k * (1)/(tanx)\\`

`= (2)/(√(3)) * (1)/(tan 60)\\\\= (2)/(√(3)) * √(3)\\\\=2`

Answer 2

When something is inversely proportional it can be solved by using the equation:

y = k/x

where k is the constant.

So using this we can plug in x and y to find the value of k.

3 = k/4.

Next we isolate k and find that k = 12. Now we use this to find the value of y when x = 8. Plug in x and you get y = 12/8 or y = 3/2 or 1.5.

Another way to solve this is to look at how the value of x changes. When the value of x goes up, the value of y goes down.

In other words, when x is multiplied by some number, y is divided by that number. In this equation we can see that x is multiplied by 2 to go from 4 to 8.

Thus, y must be divided by 2.

Thus, y = 3/2 or 1.5.