which is equal to sin(-120)?

Question

sin 60, -sin 60, cos 30, -sin 30........................ how do i find this out iwthout a calculator... please help

Answer 1

You need two rules of calculation:

sin(-x) = -sin(x)
and
sin(x) = sin(180-x)

so:
sin(-120) = -sin(120) = -sin(180-120) = -sin(60)

Answer 2

There are a couple of different ways. First of all, sin(-x) = -sin(x). You can verify this by looking at the graph of a sine wave. So sin(-120) = -sin(120). You can also use the formula sin(2x) = 2sin(x)cos(x), so -sin(120) = -2sin(60)cos(60), or -2*sin(60)*(1/2) = -sin60.

The technique I've always used for these kinds of problems is to 1) find out which quadrant the angle ends up in (measured from the positive side of the x-axis), then 2) take the projection of this angle on to the x-axis, and finally 3) remember the trig functions that give positive values for this follow the line "ASTC" or the mnemonic "All Students Take Calculus". In the first quadrant "All" of the six trig signs give positive answers. In the second quadrand only sin (the "S" in "Students") and csc are positive. In the third quadrant, it's only tan (the "T" in "Take") and cot, and in the fourth it's only cos and sec.

So for example, -90 degrees puts us on the bottom half of the y-axis, and minus another 30 degrees puts us in the third quadrant. So that's where -120 degrees is. The angle between this line and the part of the x-axis in the same quadrant is 60 degrees. Sin is negative in the third quadrant, so the final answer is -sin(60).

Answer 3

-sin(60)

There are 2 triangles whose sides you have to know. First is the 30-60-90 with sides 2, sqrt(3), and 1. Second is the 45-45-90 with sides 1,1,and sqrt(2).

There are two ways I can think of to figure it out, both require looking at a graph.

A careful graph of sin(x) and cos(x), studied from the periodic perspective would help. Do something like graph sin(x) and y= 1/2 to see where they intersect.

The second one requires graphing the unit circle and labeling all of the points.

http://en.wikipedia.org/wiki/Image:Unit_circle_angles.svg

Gotta think of sine as relating to y and cosine as relating to x for that to help.

Answer 4

First,sketch a equilateral triangle with each side 2 unit.
Divide it into two symmetrically.
You should get 2 triangles with base 1unit,height 3^1/2unit,and hypotenuse 2unit.
Since its a equilateral triangle,when you divide it into 2,the top angle will be 30,60 and 90 respectively.
Just use the numbers and play around.
For example,
sin30=1/2
cos30=(3^1/2) / 2
And remember sin(90-a)=cos(a) where a is 0

Answer 5

The reference angle is 60 degrees, but being in Quad III means it's negative, so -sin60.

Answer 6

sin 60

when it says sin of a negative number, you go around the circle backwards. when you go 120 degrees around the circle backwards, it is the same as 60 degrees going frontwards. hope this helps.