SOLUTION: Asked this question last night but forgot a portion of the problem. If given SinA = -5/7 and 180° < A < 270° Find: Sin(2A), Cos(2A), and Tan(2A) I have the formula and am

Algebra ->  Trigonometry-basics -> SOLUTION: Asked this question last night but forgot a portion of the problem. If given SinA = -5/7 and 180° < A < 270° Find: Sin(2A), Cos(2A), and Tan(2A) I have the formula and am      Log On


   



Question 1073744: Asked this question last night but forgot a portion of the problem.
If given SinA = -5/7 and 180° < A < 270°
Find: Sin(2A), Cos(2A), and Tan(2A)
I have the formula and am working through it but feel like my numbers are coming out wrong.

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

Since we are given 180° < A < 270°, we know A is in QIII, so we
draw angle A in QIII, and since +SINE=OPPOSITE%2FHYPOTENUSE=y%2Fr,
we can put angle A in a right triangle in QIII with OPPOSITE=y as 
the numerator -5 and the denominator as the HYPOTENUSE=r as 7.  
(We always take the hypotenuse r as positive.

Then we find the adjacent side, x, by the Pythagorean theorem:

r%5E2=x%5E2%2By%5E2
7%5E2=x%5E2%2B%28-5%29%5E2
49=x%5E2%2B25
24=x%5E2
%22%22+%2B-+sqrt%2824%29=x
%22%22+%2B-+sqrt%284%2A6%29=x 
%22%22+%2B-+2sqrt%286%29=x


Now you can use your formula
We know to take the negative sign since
x goes to the left.

-2sqrt%286%29=x

 

Now use your formulas for 2A using OPPOSITE, ADJACENT and HYPOTENUSE from
the triangle graph above.  Be sure to use the correct signs.  The
ADJACENT or x in QIII is negative (because it goes left) and the OPPOSITE 
or y in QIII is also negative (because it goes down). The hypotenuse r is 
ALWAYS positive in every quadrant.

If you still get the wrong answers, tell me in the thank-you note form
below and I'll get back to you by email.  No charge ever! I do this for fun.

Edwin