Mathematics
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OpenStudy (zab505):
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OpenStudy (zab505):
OpenStudy (zab505):
@zzr0ck3r
OpenStudy (zzr0ck3r):
I agree with @jim_thompson5910
OpenStudy (zab505):
I did
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jimthompson5910 (jim_thompson5910):
do you see the identity where it lists tan(x/2) ?
OpenStudy (zab505):
I belief so
jimthompson5910 (jim_thompson5910):
if sin(x) = -3/5 and we're in Q3, what is cos(x) ?
OpenStudy (zab505):
not sure
jimthompson5910 (jim_thompson5910):
use the idea that sin^2 + cos^2 = 1
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OpenStudy (zab505):
Sorry I'm so lost
jimthompson5910 (jim_thompson5910):
sin^2 + cos^2 = 1
(-3/5)^2 + z^2 = 1
solve for z
OpenStudy (zab505):
+,-4/5
jimthompson5910 (jim_thompson5910):
we're in Q3, so is cosine positive or negative?
OpenStudy (zab505):
Negative
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jimthompson5910 (jim_thompson5910):
that means
sin(x) = -3/5
cos(x) = -4/5
jimthompson5910 (jim_thompson5910):
plug those into the tan(x/2) formula and simplify
OpenStudy (zab505):
How?
jimthompson5910 (jim_thompson5910):
\[\Large \tan \left(\frac{x}{2}\right) = \frac{1-\cos(x)}{\sin(x)}\]
\[\Large \tan \left(\frac{x}{2}\right) = \frac{1-\left(-\frac{4}{5}\right)}{-\frac{3}{5}}\]
\[\Large \tan \left(\frac{x}{2}\right) = ???\]
OpenStudy (zab505):
x=-2.49 and -4.39
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jimthompson5910 (jim_thompson5910):
idk how you're getting that
jimthompson5910 (jim_thompson5910):
and you're supposed to get one answer only
OpenStudy (zab505):
tan(1/2x)
jimthompson5910 (jim_thompson5910):
All you're doing at this point is simplifying
\[\Large \frac{1-\left(-\frac{4}{5}\right)}{-\frac{3}{5}}\]
OpenStudy (zab505):
Just forget it
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jimthompson5910 (jim_thompson5910):
\[\Large \frac{1-\left(-\frac{4}{5}\right)}{-\frac{3}{5}}\]
\[\Large \frac{\frac{5}{5}+\frac{4}{5}}{-\frac{3}{5}}\]
\[\Large \frac{\frac{5+4}{5}}{-\frac{3}{5}}\]
\[\Large \frac{\frac{9}{5}}{-\frac{3}{5}}\]
what's next?
OpenStudy (zab505):
-3! I'm so sorry for everything.
jimthompson5910 (jim_thompson5910):
that's ok