Download Trigonometric Functions on the Coordinate Plane

August 26, 2014
Trigonometric Functions on the Coordinate Plane
(x, y)
"point (x, y) lies on terminal side" means:
y = opposite side
x = adjacent side
Aug 26­7:57 AM
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
Quad II
(­x, y)
(x, y)
Quad IV
Quad III
(x, ­y)
(­x, ­y)
Sep 3­8:24 AM
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August 26, 2014
All Students Take Calculus
S
A
T
C
Tells you which function should be positive in each quadrant
Sep 3­8:30 AM
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.
Aug 26­7:58 AM
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August 26, 2014
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.
Aug 26­7:59 AM
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 sin θ = 4/5, find the values of the remaining five trigonometric functions.
Aug 26­8:02 AM
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August 26, 2014
4. 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.
Aug 26­8:04 AM
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