Question

The equation sin ( (PI/3) - x ) is equal to ____.
A. 1/2( sqrt(3) cosx + sinx)
B. 1/2(sqrt(3) cosx - sinx)
C. 1/2(cosx- sqrt(3) sinx)
D. 1/2 (cosx + sqrt(3) sinx)

Answer 1

The Angle Difference Formula for Sine tells us that...
\[\large \sin(\alpha-\beta)=\sin \alpha \cos \beta- \sin \beta \cos \alpha\]

Answer 2

Applying this to our problem gives us...
\[\large \sin(\frac{ \pi }{ 3 }-x)=\sin\frac{ \pi }{ 3 }\cos x- \sin x \cos\frac{ \pi }{ 3 }\]

Answer 3

From there, you'll need t remember your special angles.. One of them is 1/2, the other is going to be sqrt3/2, you'll have to figure out which is which. :D

After you fill in the pieces, you'll be able to factor 1/2 out of each term, and it should match one of your answers. Yay!

Answer 4

...you say yay ..im still like wat? ..

Answer 5

lolol, confused on what part? :O

Answer 6

all of it ._.

Answer 7

We started with a problem that contains a weird looking angle (The thing inside the sine function is an angle, we apply trig functions to angles).

We have a formula that allows us to mess with the angle, split it up into pieces :O

Hmmm trig is a little tricky to explain c:

Answer 8

In the formula that I stated earlier, in our problem the corresponding pieces are
\[\huge \alpha = \frac{ \pi }{ 3 }, \beta= x\]

Answer 9

..yeah it is :/ um what?

Answer 10

You've learned these formulas yes? :O Just confused on how to apply them?