question 6\nfind the sine and cosine of the angle ( t ) in ( (0,2 pi) ), in standard position, whose…

question 6\nfind the sine and cosine of the angle ( t ) in ( (0,2 pi) ), in standard position, whose terminal side intersects\nthe unit circle at the point ( p=left(\frac{sqrt{2}}{2},-\frac{sqrt{2}}{2}\right) ). answer exactly.\n\n( sin (t)= )\n( cos (t)= )\nquestion help: ( square ) message instructor

question 6\nfind the sine and cosine of the angle ( t ) in ( (0,2 pi) ), in standard position, whose terminal side intersects\nthe unit circle at the point ( p=left(\frac{sqrt{2}}{2},-\frac{sqrt{2}}{2}\right) ). answer exactly.\n\n( sin (t)= )\n( cos (t)= )\nquestion help: ( square ) message instructor

Answer

Explanation:

Step1: Recall the definition of sine and cosine on the unit circle

For a point (P=(x,y)) on the unit circle (x^{2}+y^{2} = 1) and an angle (t) in standard position whose terminal side passes through (P), we have (\sin(t)=y) and (\cos(t)=x).

Step2: Identify (x) and (y) coordinates of point (P)

Given (P=\left(\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2}\right)), here (x = \frac{\sqrt{2}}{2}) and (y=-\frac{\sqrt{2}}{2}).

Answer:

(\sin(t)=-\frac{\sqrt{2}}{2}) (\cos(t)=\frac{\sqrt{2}}{2})