find the value of all other five trigonometric functions from the given functions sinx=5/13, cosx>0 and cosx=-4/5,sinx>0. thanks!

Question

find the value of all other five trigonometric functions from the given functions sinx=5/13, cosx>0 and cosx=-4/5,sinx>0. thanks!

Answer 1

Hi Ck.

 

For your first function:

 

sin(x) = 5/13, cos(x) > 0

 

For sine and cosine both to be positive, you must be in the first quadrant, where everything is positive.

 

Since sin = opp/hyp, that tells you the the opposite leg of your angle is 5, and your hypotenuse is 13.

 

This means your adjacent leg is:

 

√(13^2 - 5^2) = 12

 

Opp = 5

Adj = 12

Hyp = 13

 

So, from SOHCAHTOA:

 

sin(x) = 5/13

cos(x) = 12/13

tan(x) = 5/12

 

csc(x) = 13/5

sec(x) = 13/12

cot(x) = 12/5

 

From your second function:

 

cos(x) = -4/5, sin(x) > 0

 

For cosine to be negative and sine to be positive, you must be in the second quadrant, so the adjacent leg will be negative and the opposite leg will be positive. Sine will remain positive, but cosine and tangent will be negative.

 

Since cos(x) = adj/hyp, and cos(x) = -4/5, that means that your adjacent leg is -4, and your hypotenuse is 5.

 

This means your opposite leg is:

 

√(5^2 - (-4)^2) = 3

 

Opp = 3

Adj = -4

Hyp = 5

 

sin(x) = 3/5

cos(x) = -4/5

tan(x) = -3/4

 

csc(x) = 5/3

sec(x) = -5/4

cot(x) = -4/3

 

Hope this helps.