trig gurus I need your help......I am sick at home studying for a test that is taking place tomorrow?

Question

here is the question; determine the value of (2,-2)

sinΘ=
cosΘ=
tanΘ=

please someone help me?

Answer 1

Solve for the hypotenuse of the triangle formed by the point (2,-2) with the origin:

2^2 + (-2)^2 = sqrt(8) = sqrt(4)sqrt(2) = 2sqrt(2)

cos = -2/(2sqrt(2)) => multiply by sqrt(2)/sqrt(2) to get rid of the radical in the denominator
cos = -2sqrt(2) / 2sqrt(2)sqrt(2)
= -sqrt(2) / 2

sin = 2/2sqrt(2)
sin = sqrt(2)/2
tan = -2/2
tan = -1

Answer 2

The only thing that I can come up with is in a Cartesian coordinate system, draw a line from 0 to (2, -2) and call the angle it forms with the x-axis Θ. In that case, Θ = -45 degrees, and you get the following values.

sinΘ = 1/sqrt(2)
cosΘ = -1/sqrt(2)
tanΘ = -1

Answer 3

The y coordinate is negative and the x value is positive so the point is at quadrantIV.
Draw a line from the origin to that point.
The slope would be -1.
At this quadrant sin is negative and cos is positive and tan is negative.
The at that point tan should be -1
Now x=rcostheta
r is the length from the origin to 2,-2
Find the distance and it is 8^1/2 or 2*2^1/2
Divide x by 2root2
Looks like 1/root2
That is costheta
y=rsintheta
sin theta=-1/root2
There is a high possibility I could be wrong =O.

Answer 4

It will help if you first draw an x-y coordinate system with the point (2,-2) marked on it. Now draw a line from (0,0) to (2,-2). Now draw a vertical line from (2,-2) to the x-axis.

You should now have a right triangle that you can use trig for.

The hyp. of this triangle equals the squareroot of (2^2 + 2^2) = 2(sqrt2)

We also know that:

sin = opp. / hyp.
cos = adj. / hyp.
tan = opp. / adj.

so:

sin = -2 / 2sqrt2 = -1 / sqrt2
cos = 2 / 2sqrt2 = 1 / sqrt2
tan = -2 / 2 = -1

I think this is what the question is asking for.

Answer 5

yeeeehaw's answer is almost correct. Given that is the question you are asking as he states it. But the signs for the answers for sin and cos are reversed. Cos is a positive number (side adjacent to the angle over the hypotenus) and sin is a neg number (side opposite over the hypotenus). Side adjacent to the angle formed by (2,-2) and the origin is 2. Side opposite is -2.

Answer 6

Google says sin=0, cos=1, tan=0