Find the trig value

Question

Use knowledge of trig identities to find the trig value below.

If csc α = 5/2 , find sec α cot α

Answer 1

secαcotα = (1/cosα)(cosα/sinα) = 1/sinα

 

                                            = cscα = 5/2

Answer 2

 

The trig definitions are:

 

cos(α)=x/r >>sec(α)=r/x

 

sin(α)=y/r >> csc(α)=r/y

 

tan(α)=y/x >> cot(α)=x/y

 

 

Using the unit circle, where x²+y²=r²

 

if csc(α)=5/2, then r=5, and y=2

 

so to find x,

 

5²=x²+2²

 

√(21)=x

 

sec(α)=r/x=5√(21)/21

 

cot(α)=x/y=√(21)/2

 

 

Answer 3

csc α = 5/2 ⇒ sin α = 2/5

sin α = 2/5 ⇒ cos √21
cos α = √21 ⇒ sec √21/21

 

Can you determine tan α and cot α?