SOLUTION: If cos x= -15/17 with x in quadrant III, find the exact value of sin 2x and the quadrant of 2x

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Question 1161413: If cos x= -15/17 with x in quadrant III, find the exact value of sin 2x and the quadrant of 2x
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
If cos+%28x%29=+-15%2F17+with x+in quadrant III, find the exact value of sin+%282x%29 and the quadrant of 2x
given:
cos+%28x%29=+-15%2F17+
find:
sin+%282x%29
use identity:
sin%282x%29=2sin%28x%29cos%28x%29 ......substitute cos
sin%282x%29=2sin%28x%29%28-15%2F17%29+

use sin%28x%29=sqrt%281-cos%5E2%28x%29%29 to find sin
sin%28x%29=sqrt%281-%28-15%2F17%29+%5E2%29
sin%28x%29=sqrt%281-225%2F289%29
sin%28x%29=sqrt%28%28289-225%29%2F289%29
sin%28x%29=sqrt%2864%2F289%29
sin%28x%29=±8%2F17%29

In Quadrant III, sine and cosine are negative:
sin%28x%29=-8%2F17
then
sin%282x%29=2%28-8%2F17%29%28-15%2F17%29+
sin%282x%29=240%2F289
2x=sin%5E-1%28240%2F289%29
2x=56.14° -> In Quadrant I


Answer by MathTherapy(10553) About Me  (Show Source):
You can put this solution on YOUR website!

If cos x= -15/17 with x in quadrant III, find the exact value of sin 2x and the quadrant of 2x
You may be able to recognize this TRIG function as an 8-15-17 PYTHAG. TRIPLE.

We have: 

As x is in QIII, we get: y = O = - 8, and so, 

matrix%281%2C3%2C+sin+%282x%29%2C+%22=%22%2C+2+sin+%28x%29+cos+%28x%29%29



Can you now tell which quadrant 2x lies in?