Find the exact values

Question

Find the exact value of the trig function given that sin u = 4/5 and cos v = -7/25 

Both angles are in quadrant 2 

Tan(u-v)

Answer 1

 

Hi Cierra,

 

Remembering that sin(·) and cos(·) are positive and negative,

 

respectively, in the second quadrant,

 

from either the Pythagorean theorem or

 

the formula sin²θ + cos²θ = 1,

 

we can find out the value of cos(u) and sin(v).

 

   sin(u) = 4/5, cos(u) = -3/5   ⇒   tan(u) = -4/3

 

   sin(v) = 24/25, cos(v) = -7/25   ⇒   tan(v) = -24/7

 

Plugging in the above values into the trigonometric identy

 

   tan(u-v) = [tan(u) - tan(v)]/[1 + tan(u)·tan(v)]

 

                = [(-4/3) - (-24/7)]/[1 + (-4/3)·(-24/7)]

 

                = (-4/3 +24/7)/[1 + (4/3)·(24/7)]

 

                = (44/21)/[1 + (96/21)]

 

                = 44/117

 

Hope this helps.