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hi, my final is tonight and I'm trying to study up.

if cot x 3/7
and sin x < 0
evaulate cos 2x exactly

thanks a lot for any help!

2007-12-06 03:54:13 · 4 answers · asked by Nate 6 in Science & Mathematics Mathematics

cot x = 3/7!

2007-12-06 04:05:49 · update #1

sorry................

2007-12-06 04:06:01 · update #2

4 answers

cot(x) = adjacent side /opposite side

since cot(x) = 3/7

so adj. side = 3 and

opposite side = 7

hypotenuse = sqrt(opp.side^2 + adj.side^2)

hypotenuse = sqrt(49 + 9) = sqrt(58)

so sin(x) = opp. side/hypotenuse = - 7/sqrt(58) (since sin(x)<0)

now cos(2x) = 1 - 2sin^2(x)

cos(2x) = 1 - 2(-7/sqrt(58))^2

cos(2x) = 1 - 2(49/58)

cos(2x) = 1- 49/29

cos(2x) = -20/29

2007-12-06 04:13:17 · answer #1 · answered by mohanrao d 7 · 0 0

cotx = 3/7 which is positive
sinx < 0 and since cotx = cos/sin then cos x must be negative also. Quadrant III

cotx = adj/opp and by pythagorean theorem, this makes the hypotenuse = sqrt(3^2 + 7^2) = sqrt(58)

then sinx = opp/hyp = -7/sqrt58
cos 2x = 1 - 2sin^2x
cos2x = 1 - 2(-7/sqrt58)^2
cos2x = 1 - 2(49/58 )
cos 2x = 1 - 49/29
cos 2x = -20/29

2007-12-06 04:13:03 · answer #2 · answered by Linda K 5 · 0 0

If cotx > 0 and sinx<0, then x terminates in the third quadrant.
A quick sketch and the Pythagorean Theorem reveals that
cos(x) = -3/sqrt(58). But cos(2x) = 2cos^2(x) - 1, so substituting, cos(2x) = -20/29, upon reducing the resulting fraction.

2007-12-06 04:02:02 · answer #3 · answered by Anonymous · 0 0

help us help you
what do you mean by
cot x 3/7
if it was a simple fraction, it would come before the x, yes?
is the 3/7 an exponent?
use parentheses and brackets like cot[(3/7)x]
or the carat sign, "^" (shift 6), to denote an exponent and use parentheses there as well like cot[x^(3/7)]
anybody who tries to answer without knowing specifically will be working an answer and most likely in the wrong direction.
standing by!

2007-12-06 04:04:44 · answer #4 · answered by Jim L 3 · 0 0

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