Topics:
• Angles in the coordinate plane in standard position
• The coordinate plane definitions of the trig functions
• Coterminal angles
• Radian measure for angles (very important!)
Important note: There will be one more definition of the trig functions, which comes from this, and it is the most important one, so make sure you learn these right away!
You must learn the two special right triangles and the definitions of the trig functions by heart!
VOCABULARY TO KNOW:
angle (as a rotation)
angle in standard position
positive angle
negative angle
initial side
terminal side
coterminal angles
THE COMPLETE DEFINITIONS OF THE 6 TRIGONOMETRIC FUNCTIONS IN THE COORDINATE PLANE:
$\theta$ is an angle in standard position, $(a,b)$ is a point on the terminal side of $\theta$, and $r$ is the distance from the origin to $(a,b)$: $r = \sqrt{a^{2}+b^{2}}$
Then define the six trigonometric functions as:
sine: $\sin\left(\theta\right) = \frac{b}{r}$
cosine: $\cos\left(\theta\right) = \frac{a}{r}$
tangent: sine: $\tan\left(\theta\right) = \frac{b}{a}$
secant: sine: $\sec\left(\theta\right) = \frac{r}{a}$ (the reciprocal of cosine)
cosecant: $\csc\left(\theta\right) = \frac{r}{b}$ (the reciprocal of sine)
cotangent: $\sin\left(\theta\right) = \frac{a}{b}$ (the reciprocal of tangent)
Homework:
• There are two new WeBWorK assignments. It is recommended that you do them in the following order;
(1) Coordinate plane trig
(2) Angle measure – radians
• I will post some problems from the textbook which you may put on the board at the start of class when I have a chance to look through them. Stay tuned!
Remember that if you get stuck on any of the problems or have a question about any of the material, you can post a question to the Piazza discussion board.
In case you prefer to view videos on any of these topics, Here is a copy of the Course Outline with links to video resources for each topic.
