Day 3: Trigonometric Equations & Quadrantal Angles

Hello Everyone! HAPPY HALLOWEEN!!!!! This is Alyana scribing for today. Today we didn't really learn anything new. Anyways, this is what we discuss in class.

The trigonometric functions cosine and sine may be defined on the unit circle as follows. If (x,y) is a point of the unit circle, and if the ray from the origin (0,0) to (x,y) makes an angle theta from the positive x-axis,
then cos(t) = x
sin(t) = y

The equation x2+ y2 = 1 gives the relation
cos2(t) + sin2(t) = 1

P(t)=(x,y) radius is equal to 1 = (cos(t), sin(t)) radius is greater than 1.




Sin(t)= O/H => Sin(t)= Y/1=Y
Cos(t)= A/H => Cos(t)= X/1=X
Tan(t)= O/A => Tan(t)= Y/X= Sin(t) divide by Cos(t)

The standard position starts at (1,0).

Positive distance is measured in counterclockwise direction &
Negative distance is measured in a clockwise direction.

Review of solving Trigonometric Equations:

1. Solve the trigonometric function(sin(t), cos(t) or tan(t))
2. Find the related angle by using the inverse trig function on the positive guy only.
3. Find the quadrants based on the sign of the trig guy (use the C.A.S.T. rule)
4. Find the solution in each quadrant determined in step 3.
5. Write your solution.
   

QUADRANTAL ANGLES <;3
An angle in standard position with terminal side lying on x-axis or y-axis is called as Quadrantal Angle. The terminal side is on an axis: 0 degree, 90 degrees, 270 degrees, 360 degrees ....

I'm not good at blogging
Sorry... oh well... hope this helped you guys a little :D