Is there a formula?
2007-01-11 10:23:21 · 8 answers · asked by stardust6547 2 in Science & Mathematics ➔ Mathematics
The sine function is periodic, with period 360 deg. So subtract multiples of 360 from 765 until you get something nonnegative and less than 360; this is 45 degrees. So 765 deg and 45 deg have the same sine, which is ___.
P.S. There is no real formula, just add/subtract multiples of 360, and use the reference angle method. In Quadrant I, the reference angle is the same angle as the angle you're computing the sine of. Alpha = theta. In Quadrant II, the ref. angle is the supplement of the angle. Alpha = 180 deg - theta. For Quadrant III, subtract 180 degrees; alpha = theta - 180 deg. And for Quadrant IV, subtract _from_ 360 degrees: alpha = 360 deg - theta.
2007-01-11 10:32:39 · answer #1 · answered by Anonymous · 1⤊ 0⤋
First you can sustract any multiple of 360, so 765 bolis down to 765-720=45. Aren't you happy? It's approximately
0.707 10 678 11. or sqrt{2} / 2
2007-01-11 10:29:32 · answer #2 · answered by gianlino 7 · 1⤊ 0⤋
sin(765 degrees) is the same as sin(45 degrees)
subtract 765 by 360 enough times until it becomes less than 360
765 - 360 = 405
405 - 360 = 45
sin(45 degrees) is exactly (√2)/2
2007-01-11 10:29:01 · answer #3 · answered by Anonymous · 1⤊ 0⤋
Since sine has a period of 360 degrees, you have
sin(x) = sin(x + 360n), where n is any integer.
We can write 765 as 45 + 720 = 45 + 360*2
sin(765) = sin(45 + 360*2) = sin(45) = sqrt(2) / 2
2007-01-11 10:28:38 · answer #4 · answered by MsMath 7 · 2⤊ 1⤋
The first thing to do is convert it to radians. This is done by multiplying the number in degrees by pi/180.
765pi/180 = 153pi/36 = 51pi/12 = 17pi/4
However,
sin(17pi/4) = sin(17pi/4 - 2pi) {since adding or subtracting by 2pi does not change the location on the unit circle}.
sin(17pi/4 - 8pi/4) = sin(9pi/4)
Let's go around the circle again, backwards, by subtracting 2pi once again.
sin(9pi/4 - 2pi) = sin(9pi/4 - 8pi/4) = sin(pi/4)
Now we have a value which we know on the unit circle.
sin(pi/4) = sqrt(2)/2
2007-01-11 10:29:32 · answer #5 · answered by Puggy 7 · 1⤊ 0⤋
The sine of 765 is the square root of two divided by two.
2007-01-11 10:29:10 · answer #6 · answered by The answer guy 3 · 1⤊ 1⤋
sqrt2/2 is correct. You don't want to use the calculator; it gives and approximate answer. Memorize the values on the unit circle, it will save you a lot of time.
2007-01-11 10:38:36 · answer #7 · answered by anr 3 · 0⤊ 1⤋
use a calculator
2007-01-11 10:31:56 · answer #8 · answered by Rick 5 · 0⤊ 1⤋