Answer:
[tex]\frac{(-\sqrt{6}-\sqrt{2} )}{4}[/tex]
Step-by-step explanation:
hey there,
< Use trigonometric identities for these kinds of problems.
First, we have 19π/12. Clearly, we don't know what the value of this is so we will have to use subtraction or addition of things we do know. Things we do know are the angles 30, 45, and 60 degrees. We also know these angles in different quadrants, like 330 degrees.
Basically, you have to look at your unit circle and just find two values that will be able to add/subtract to get what you need.
After looking at the unit circle, I decided to use 4pi/3 + pi/4. If you add them up, it makes 19pi/12.
So, if I put them in, it would be [tex]sin(\frac{4pi}{3} + \frac{pi}{4} )[/tex].
You have to use a trigonometric identities chart to know what to do next (just search one up).
For identities like this one (sin(x+y)), here is what it will always equal:
sinxcosy+cosxsiny
So let's use that in our problem. x = 4pi/3 and y = pi/4.
...
Once you have put them in, use your triangles and find out what each one equals! Then continue solving my multiplying.
After solving, you will later get the answer [tex]\frac{(-\sqrt{6}-\sqrt{2} )}{4}[/tex]. >
Sorry I couldn't explain very well, but I hope this helped. Feel free to ask anything else.
