Chapter 4 - Trigonometry & Unit Circle
What are the 3 secondary trig ratios? What are they?
- they are reciprocals of the primary trig ratios
What are the two requirements for a unit circle?
1 Origin at (0,0) 2 Radius of 1
What is the definition of a radian?
One radian is the measure of the angle formed when the arc length of a circle has the same length as the radius of the circle.
What is the formula for arc length of a circle? What is a common error?
a = 𝜃 x r where 𝜃 is always in radians **** Common error: Do NOT plug in degrees!!!!****
How do you relate cos and sin to the x and y coordinates of a point on the unit circle?
cos 𝜃 = x sin 𝜃 = y
What is tan 𝜃 in terms of coordinates on the unit circle?
tan 𝜃 = y/x
What is the equation of the unit circle?
x² + y² = 1
What is the general form for coterminal angles of 50º?
𝜃 = 50º + 360ºk, k E I
What is the relation between angle and arc length on the unit circle, and why?
- They are the same! Because the radius is 1, a=r(𝜃 ) so a=𝜃.
What is the definition of a coterminal arm?
Angles in standard position that have the same terminal arm; at the same location on the unit circle. Found by adding or subtracting multiples of 360º.
When determining the coordinates of a circle with a given radius and x or y coordinate, what is important to remember about the missing coordinate?
Depending on its quadrant, it could be positive or negative!!!!
Any angle, 𝜃 has a ______ number of coterminal angles.
Infinite !
What is any angle measurement without units?
Radians.