I am going to ask this again, I need help with my trig I have a test that I am studying for and really can use

Question

some help.

please help me?
determine the value of
sin theta
cos theta
tan theta
if theta is a postion angle of the given point
express in simplest radical or fractional form. YOur help is appreciated, thank you
(-3,3)
how do you get that
please give me the details
the answer is 2 root 2

Answer 1

When you do this on regular graph paper, one vertex of the angle is understood to start at (0,0) and extend along the x-axis (y=0). Now, from (0,0) draw a line to -3,3. Call the enclosed angle theta. And from (-3,3) draw a line to (0,3). You now have a triangle. Two of the sides are 3 units long and there is a right angle. Thus the angle theta is a 45 degree angle. For 45/45/90 triangles, the 2 sides and hypotenuse have the ratios of 1:1:sqrt(2) respectively (this follows from Phythag. Thm). From the definition of each function, you get: for Sin = 1/(sqrt 2) or sqrt(2)/2 and the same for Cos. For tangent, the value is 1.

Answer 2

The point (-3,3) is 135° counterclockwise from the positive x-axis. It's reference angle is 45°, for which sin and cos are both (√2)/2, and tan is 1. Since the point is in quadrant 2, cos is negative while sin is positive, and that makes tan negative as well. So

sin Θ = (√2)/2
cos Θ = -(√2)/2
tan Θ = -1

Answer 3

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