Find all six trigonometric function values given cos x=7/12 and 3pi/2<x<2pi

Question

need help solving

Answer 1

Since we have to use all 6 trig functions, lets get the sinx and tanx values.

 

Using the identities:

 

1)  sin² + cos²x = 1

2)  tanx = sinx / cosx

 

So

 

sinx = √(1 - cos²x)

       = √(1 - (7/12)²)

       = √(1 - 0.5833)

       = 0.8122

 

 

cosine is positive in the 4th quadrant in the given range.  sine and tangent are negative in the 4th quadrant in this given range.

 

If cosx = 7/12,  then   x = 0.94796

 

If sinx = 0.8122 , then  x = 2π - 0.94791 = 5.33527

 

 

tanx = sinx / cosx

 

 

Buy using the values of cosine and sine, we can get tangent.

 

tanx = -0.8122 / 0.94796

tanx = -0.85679

 

then     x = 2π - 0.85679 = 5.4264

 

So far, we have 3 functions.

 

cosx = 7/12

sinx = -0.8122

tanx = 5.4264

 

 

To get the remaining 3, use the inverse of each function.