If ;
P = ( sin 4∏/3 cos∏2 /3 + cos ∏4 / 3 sin 2∏ /3 ) / (cos 5∏/4cos(-3∏/4) + sin5∏/4 sin(-3∏/4) , What is P ?
Please if you can not help , no need to answer . Thank You
2006-11-16 06:44:28 · 4 answers · asked by Asker 1 in Science & Mathematics ➔ Mathematics
Well Dear Asker ;
If P = ( sin 4∏/3 cos∏2 /3 + cos ∏4 / 3 sin 2∏ /3 ) / (cos 5∏/4cos(-3∏/4) + sin5∏/4 sin(-3∏/4)
=[ ( -sin∏/3)(-cos∏/3) + ( -cos∏/3)(sin∏/3) ] / [ (-cos∏/4)(cos3∏/4) + (-sin∏/4)(-sin3∏/4) ]
= [√3/2 * 1/2 - 1/2 * √3/2 ] / [ -√2/2 * -√2/2 - √2/2 * -√ 2/2 ]
= 0 / 1 = 0
P = 0
Hope it helps you
Good Luck dear
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2006-11-16 06:47:24 · answer #1 · answered by sweetie 5 · 4⤊ 0⤋
If P = ( sin 4â/3 cosâ2 /3 + cos â4 / 3 sin 2â /3 ) / (cos 5â/4cos(-3â/4) + sin5â/4 sin(-3â/4)
=[ ( -sinâ/3)(-cosâ/3) + ( -cosâ/3)(sinâ/3) ] / [ (-cosâ/4)(cos3â/4) + (-sinâ/4)(-sin3â/4) ]
= [â3/2 * 1/2 - 1/2 * â3/2 ] / [ -â2/2 * -â2/2 - â2/2 * -â 2/2 ]
= 0 / 1 = 0
P = 0
2006-11-16 06:50:51 · answer #2 · answered by Anonymous · 0⤊ 3⤋
The answer is zero...
It might be easier to see it in degrees:
P = [ sin(240) cos(120) + cos(240) sin (120) ] / ...
P = [ -sqrt(3)/2 * -1/2 + -1/2 * sqrt(3)/2 ] / ...
P = [ sqrt(3)/4 - sqrt(3)/4) ] / ...
P = 0 / ...
P = 0
You don't even have to look at the denominator.
2006-11-16 06:50:41 · answer #3 · answered by Puzzling 7 · 0⤊ 0⤋
The top part should bring to your mind the the equality
sin(a+b) = sina cosb + cosa sinb
If you can recognize this it becomes obscenely easy... The top part is equal to sin(4pi/3 + 2pi/3) = sin(2pi) = 0.
There's your answer! Well, not quite... you need to check that the bottom part isn't zero as well. This should remind you of another equality:
cos(a-b) = cosa cosb + sina sinb
So this is equal to cos(5pi/4 + 3pi/4) = cos(2pi) = 1.
Answer: 0/1 = 0.
2006-11-16 06:50:55 · answer #4 · answered by Anonymous · 0⤊ 0⤋