Special Angles and Trigonometric Functions 1 (Continued)

Hey everyone it's Warren.

Today in class, we continued the lesson about Special Angles and learned how to fill in the Special Angles Chart. The first three angles (30°, 45°, 60°) can be found by using the reference triangles with these angles. 90°, 180°, 270°, and 360°/0° are Quadrantal Angles, and you have to look at the (x,y) to find cos or sin. To find the sin, cos, or tan of the other angles, just look back to 30°, 45°, or 60° and look to see which radian value it matches.

Example: You try to find the sin, cos and tan of 120°, which is equal to 2╥/3, so you look back to 60° (╥/3) and copy down those sin, cos and tan values. But remember, they may not be exactly the same because of the CAST Rule, some may be positive while others are negative.

We also learned to find points such as P(╥/6).

The first thing you do is to set up a right triangle in the unit circle with the specified angle (╥/6).

Next, label the lengths of each side of the triangle.

After, find P(╥/6) = (x,y) = (cos ╥/6, sin ╥/6)

Remember that cos = A/H and sin = O/H.

cos = A/H = √3/2 , sin = O/H = 1/2 so...

P(╥/6) = (√3/2, 1/2)

Finally, we learned to find exact values.

Example: tan5╥/3

Find 5╥/3 in the unit circle and use it to make a right triangle.

Because it is 5╥/3, you know that the central angle will be 60°, label the sides of the angle accordingly (O = √3, A = 1, H = 2).

After this, we just use basic trigonometry and the CAST rule. Tan5╥/3 = O/A = √3/1 = -√3. It is negative because this is in Quadrant 4, and tan is negative.

Homework: Exercise 3 (1,2, 10-12), Exact Value Worksheet