Exact value of: Trig Function...??

[frauleinedoctor]

Finding: the exact value of this trig fxn, given that sinu = 3/4 , cosv = - 5/13 , and u and v are in quadrant II.

sin ( c + v)



So far, i have down that sin3/4 * cos3/4 + cos 3/4 * sinc - 5/13. But since these fraction dont have pi in them, I am confused as to how they fit into the problem at all...

 

[frauleinedoctor]

ooops:

sin (u + v)

 

[frauleinedoctor]

So:

sin( 3/4 - 5/13) I believe

 

[mmm4444bot]

… So far, i have down that sin3/4 * cos3/4 + cos 3/4 * sinc - 5/13 …

You've got the right identity, but you're confusing the trigonometric ratio of an angle with the measure of the angle itself.

sin(u + v) = sin(u) * cos(v) + cos(u) * sin(v)

If they tell you that sin(u) = 3/4, then you replace the expression sin(u) in the identity with the number 3/4.

You replaced sin(u) with sin(3/4), instead.

In other words, you changed the angle from u to 3/4.

With the given information, you can immediately make the following two substitutions.

sin(u + v) = (3/4) * (-5/13) + cos(u) * sin(v)

Now you need to use the fact that both angles u and v are in Quadrant II, along with your knowledge of reference triangles or the circular functions related to the unit circle (any method that you've been taught), to determine the values of cos(u) and sin(v).

After you find their values, substitute them into the identity, as well.

Then it's simply a matter of doing the arithmetic to simplify the sum of the two products into a single fraction.

If you do not know how to find the values of cos(u) and sin(v), then you've apparently fallen behind in your class. The process is too involved for me to type out all of the lessons here.

Please see your instructor.