SOLUTION: if cosx=-12/13 and sin x>0, find tan(2x)

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Question 1056289: if cosx=-12/13 and sin x>0, find tan(2x)
Found 2 solutions by Magicmushroom, ikleyn:
Answer by Magicmushroom(1) About Me  (Show Source):
You can put this solution on YOUR website!
if cosx=-12/13 and sin x>0, find tan(2x)
Take the arccosine:
%0D%0A+x=+arccosine+%28-12%2F13%29+%0D%0A
Plug in the value of x to find tan(2x)


Answer by ikleyn(52812) About Me  (Show Source):
You can put this solution on YOUR website!
.
if cosx=-12/13 and sin x>0, find tan(2x)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

0.  The useful notice is: Since cos(x) is negative and sin(x) is positive, the angle "x" terminates in QII.


1.  Since cos(x) = -12%2F13, sin(x) = sqrt%281-cos%5E2%28x%29%29 = sqrt%281-%28-12%2F13%29%5E2%29 = sqrt%281-144%2F169%29 = sqrt%28%28169-144%29%2F169%29 = sqrt%2825%2F169%29 = 5%2F13.

    The sign is "+" at the square root, since sine is positive, according to the condition.


2.  Then tan%28x%29 = sin%28x%29%2Fcos%28x%29 = %28%285%2F13%29%29%2F%28%28-12%2F13%29%29 = -5%2F12.


3.  Finally, tan%282x%29 = %282%2Atan%28x%29%29%2F%281-tan%5E2%28x%29%29 = %282%2A%28-5%2F12%29%29%2F%281-%28%28-5%2F12%29%5E2%29%29 = %28%28-10%2F12%29%29%2F%28%281-25%2F144%29%29 = %28%28-10%2F12%29%29%2F%28%28%28144-25%29%2F144%29%29 = %28%28-10%2F12%29%29%2F%28%28119%2F144%29%29 = %28-10%2A144%29%2F%2812%2A119%29 = %28-10%2A12%29%2F119 = -120%2F119.

Solved.

For more solved similar problems on calculating trig functions see the lessons
    - Calculating trigonometric functions of angles
    - Advanced problems on calculating trigonometric functions of angles
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Trigonometry: Solved problems".