Precalc Help? Are you up to the challenge? 10 points best answer (;

If sinx= -4/5 and cosy= -12/13, and pi< x < 3pi/2, pi< y < 3pi/2 find the exact value of:

a. sin(x-y)

b. cos(x+y)

c. cos2x

d. tanx/2

I need to now how to arrive at these answers, my teacher already gave me the key. So the best explanation gets the points! Please help as much as you can!

P.S. I hate the people on here who tell people asking questions that they should do their own work. I've been studying math for a few days straight, and I need some help on this problem. Thanks & Happy New Year.

There are several parts to solving these. Each one requires a different identity, but first you need to examine the angles.

The description of angle x tells you it is in quadrant III, where the sine and cosine are both negative, and the tangent is positive. (same info for angle y). This is an important piece of info.

Now draw angle x in quadrant III. Drop a perpendicular to the x axis.
Since sin x= -4/5, make the vertical leg -4 and the hypotenuse 5. By pythag thm, the horizontal leg is -3. Now you can find all the trig functions for angle x.

Draw a separate picture for angle y. Since cos y= -12/13, the horizontal leg is -12, hypotenuse = 13, so vertical leg is -5.

Now you are prepared to solve: (simplify using the identity for each)
A)sin(x-y) = sinx cosy - siny cosx
=(-4/5)(-12/13) -(-5/13)(-3/5)
= (48/65)-(15/65)
= 33/65

B) cos(x+y)=cosxcosy-sinxsiny
=?
( use the same substitutions as above)

C) cos(2x) or cos^2(x)?

If cos(2x)= cos^2(x)-sin^2(x)
= (-3/5)^2 -(-4/5)^2
= 9/25-16/25
=-7/25

If cos^2(x)= 9/25 as above

D) tan(x/2)= sinx/(1+cosx) = (-4/5)/(1+-3/5)

= (-4/5)/(2/5)

=-2

Hoping this helps!

This problem is testing your knowledge of angle formulas. So let's start there. Someone a long time ago proved that these work, so take my word for it that:

sin(x-y)=sin(x)cos(y)-cos(x)sin(y).

cos(x+y)=cos(x)cos(y)-sin(x)sin(y).

cos(2x)=(cos(x))^2 - (sin(x))^2.

tan(x/2)=(sin(x))/(1+cos(x)).

From there can you see what to do?

you just use the identities for a,b,c,d along with cos x = - 3 / 5 and sin y = - 5 / 13

tan x = 4 / 3

eg ; cos (x + y ) = cos x cos y - sin x sin y...tan 2w = 2 tan w / [ 1 - tan²w ]...{ w = x / 2 }