Download Section 5.3: Trig Functions on the Coordinate Plane

Section 5.3: Trig Functions on the Coordinate Plane
August 25, 2015
Section 5.3: Trigonometric Functions on the Coordinate Plane
(x, y)
"point (x, y) lies on terminal side" means:
y = opposite side
x = adjacent side
Label the sides hypotenuse (h), x or y. Then state if the sine, cosine, and tangent ratios will be positive or negative in the given quadrant.
Quad I
sin
cos
tan
(x, y)
Quad III
Quad II
(­x, y)
sin
cos
tan
Quad IV
sin
cos
tan
sin
cos
tan
(­x, ­y)
(x, ­y)
Section 5.3: Trig Functions on the Coordinate Plane
All Students Take Calculus
S
A
T
C
Tells you which function should be positive in each quadrant
I. Given a point on the terminal side
*graph the point
*draw a triangle from the point
*label the two lengths you know (with appropriate signs)
*find missing side length (hypotenuse)
*use the reference angle to state the functions
1. Find the value of the six trigonometric functions for an angle θ in standard position if a point with coordinate (5, ­12) lies on its terminal side.
August 25, 2015
Section 5.3: Trig Functions on the Coordinate Plane
August 25, 2015
2.) Find the value of the six trigonometric functions for an angle θ in standard position if a point with coordinate (­3, ­1) lies on its terminal side.
II. Given 1 trig. function & the quadrant the terminal side is in.
*sketch the terminal side
*draw the reference right triangle
*label the sides you know based on the given function
*find the missing side
* use the reference angle to state the functions
3. Suppose θ is an angle in standard position whose terminal side lies in Quadrant II. If sec θ = ­√29/5, find the values of the remaining five trigonometric functions.
Section 5.3: Trig Functions on the Coordinate Plane
Homework: WS 5.3.1
August 25, 2015