Find the value of the other five trigonometric functions, given tanx= 4/11, secx<0.

Question

This is for my trig class, thanks for the help! If you could, could you please show all your work? Thanks again!

Answer 1

Dear Serenity,

 

Well, if tan(x) = 4/11, that means that x = tan^-1(4/11) = 19.98º

 

So we can calculate:

 

The simplest place to start is with the cotangent.  We know cot(x) = [1/tan(x)] 

 

So cot(x) = 11/4

 

We also know that 1 + tan²(x) = sec²(x) so that 1 + (4/11)² = sec²(x)

 

Therefore sec²(x) = 1 + (16/121) = (137/121) so that sec(x) = (137/121)^(1/2) = √(137)/11

 

Similarly, 1 + cot²(x) = csc²(x), so that 1 + (11/4)² = csc²(x)

 

csc²(x) = 1 + (121/16) = 137/16

 

csc(x) = (137/16)^(1/2) = √(137)/4

 

But sin(x) = [1/csc(x)} so that sin(x) =

 

Similarly, cos(x) = [1/sec(x)] = [11/√(137)]