Question

Given that sin=2/5 and cos<0. Find the rest of the trigonometric functions

Answer 1

`\cos x=-(√(21))/(5)\\ \\\tan x =-(2)/(√(21))\\ \\\cot x=-(√(21))/(2)`

Explanation:

Given

`\sin x=(2)/(5)\\ \\\cos x<0`

Use formula:

`\cos^2x+\sin ^2x=1\\ \\\cos^2x+\left((2)/(5)\right)^2=1\\ \\\cos^2x=1-(4)/(25)\\ \\cos^2x=(21)/(25)\\ \\\cos x=\pm (√(21))/(5)`

Since
`\cos x<0,` then

`\cos x=-(√(21))/(5)`

By definition,

`\tan x =(\sin x)/(\cos x)=((2)/(5))/(-(√(21))/(5))=-(2)/(√(21))\\ \\ \\\cot x=(1)/(\tan x)=(1)/(-(2)/(√(21)))=-(√(21))/(2)`