Question

If sinx=20/29, x lies in the second quadrant the tan x =

Answer 1

Answer:

-20 / 21

Step-by-step explanation:

Given

sin x = 20/29

Since x lies in the second quadrant

So sin x and cosec x are positive and the rest trigonometric functions are negative.

sin x = opposite side/hypotenuse = 20 / 29

Let opposite side = 20k, hypotenuse = 29k   [k is any integer]

We know that

opposite side² + adjacent side² = hypotenuse² [by Pythagoras theorem]

⇒ (20k)² + adjacent side² = (29k)²

⇒adjacent side² = k²(29² - 20²) = 441k²

∴adjacent side = 21k

∴ tan x = opposite side / adjacent side

As x is in second quadrant, tan x is negative

∴ tan x = -20k / 21k = -20/21