Trigonometry in the Coordinate Plane PART FIVE Trigonometry

Trigonometry in the Coordinate Plane PART FIVE

Trigonometry in Coordinate Plane In this last section we will use the ideas taught in the previous sections (special triangles, unit circle, CAST Rule and reference angles) along with a few more pieces of information to find all points on the unit circle that can be determined without a calculator. Let’s get started!

Trigonometry in Coordinate Plane

Trigonometry in Coordinate Plane Now we will put the 30 degree angle in the unit circle and using that as a reference angle we will find the other three angles [quadrants II (A), III (B) and IV (C)] with the same trig value as 30 changing the sign based on the CAST Rule. Remember that in the unit circle x = cos θ y = sin θ So by having the same trig values as 30 we can find the points on the unit circle for these other angles A, B and C

Trigonometry in Coordinate Plane

Trigonometry in Coordinate Plane

Trigonometry in Coordinate Plane

Trigonometry in Coordinate Plane The last points and angles we want for the unit circle are those on the x and y axis. These angles are shown on the diagram to the right – 0, 90, 180, 270 Since this is a unit circle the radius = 1 We know then that the point at angle 0 has an x=1 and a y=0 We can similarly reason out the points for 90, 180 and 270 also shown in the diagram.

Trigonometry in Coordinate Plane Sometimes we can allow ourselves to move along without realizing the importance of what we’ve done. I don’t want that to happen here. Remember in the unit circle that x = cos θ and y = sin θ That means we just found the following: cos 0 = 1, sin 0 = 0 cos 90 = 0, sin 90 = 1 cos 180 = -1, sin 180 = 0 cos 270 = 0, sin 270 = -1 And 360 is the same as 0 so cos 360 = 1, sin 360 = 0

Trigonometry in Coordinate Plane To summarize, we now know all these angles and their points on the unit circle 0 30 45 60 (1, 0) 210 90 120 135 150 180 (0, 1) 225 240 270 (0, -1) 300 (-1, 0) 315 330 360 (1, 0)

STOP I KNOW THIS IS A LOY OF INFORMATION PLEASE GO OVER THESE SLIDES AGAIN (AND AGAIN IF NECESSARY) YOU WILL HAVE PRACTICE PROBLEMS TO SOLIDIFY THESE IDEAS IN EACH OF THE PARTS WHICH SHOULD HELP. ASK QUESTIONS WHEN YOU NEED TO