Suppose cos B = 1/2. Find all Values of B in degrees between -180 degrees and 540 degrees that solve this equation.
Please Show me How to do it!!
2007-03-27 17:11:20 · 4 answers · asked by Anonymous in Education & Reference ➔ Homework Help
you know that cos (angle B) = 1/2 means that angle B is equal to 60 degrees.
so.... you know cos(any angle) is positive in Quad I, because in this quadrant, sin, cos, and tan are all positive. if you go around a full 360 circle counter clockwise... you will come back to Quad I when angle is 420 degrees.... and another full circle (another 360 degrees added) would be 780 degree, back in Quad I... but that is more than your 540 degree range...
So all the Values that B is between -180 degrees and 540 degrees that land in Quad I are... 60 degrees and 420 degrees...
then you have to find out in which other quadrant/s cosine is positive and those will give the other angles using the same above process...
so cosine is also positive in Quad IV (and only cos is positive in Quad IV)... so you have -60 degrees to start with... now add another 360 degress... to -60 degrees (full counterclockwise circle) and you get 300 degrees (-60+360 = 300)...Add another 360 degrees and you get 660... but that is more than 540 degree range limit...
so you found two more angles here... -60 degs and 300 degs in Quad IV...
angles that B are in that range are 60 and 420 (both in Quad I) and -60 and 300 (both in Quad IV).
DONE
2007-03-27 17:30:11 · answer #1 · answered by blueskies 7 · 0⤊ 0⤋
I'm not exactly sure of what you are asking. The cosine of 60 degrees is .5 as is the cosine of 300 degrees. -180 = 270 and the cosine of 270 is not .5; neither is the cosine of 540 .5. -60 = 300, 420 degrees is actually 60 degrees so your valid angles are -60, 60, 300, 420 but then these are really on two angles.
2007-03-27 17:28:20 · answer #2 · answered by Anonymous · 0⤊ 0⤋
how to do it?
OK, here's how I would reason it out
cosine is positive in the first and fourth quadrants
arc cosine (.5) = 60 deg
OK..so..a 60 deg angle in the fourth quad would be 300 deg
to get the other angles, consider the period icy of the cosine...
or
check one of those theorems that state..
cos (theta + 180) = something or another in terms of cosine
see which ones fall into your range of -180 to 540
OK?
that's how to do it!
2007-03-27 17:28:14 · answer #3 · answered by Gemelli2 5 · 0⤊ 0⤋
i dont think you will find what you are loking for on here it seems like you are missing something
2007-03-27 17:15:46 · answer #4 · answered by aarika 4 · 0⤊ 0⤋