Download 2-3 notes day 1

January 27, 2015
2-3
Evaluating
Trigonometric
Functions for
Nonacute Angles
S
sine and cosecant are positive
A
All trig functions are positive
Remember: Trigonometric Functions
Let (x, y) be any point, other than the origin, on the terminal side
of an angle Θ in standard position. Let r be the distance from the
point (x, y) to the origin; then the six trigonometric functions are
defined as:
sin Θ = cos Θ =
tan Θ =
csc Θ = sec Θ =
cot Θ =
Example 1
Indicate the quadrant in which the terminal side of θ must lie in order for
each of the following to be true.
a) cosθ is negative and sinθ is positive
T
tangent and cotangent
are positive
C
cosine and secant
are positive
b) tanθ is positive and cosθ is negative
c) secθ and cscθ are both negative
A Smart Trig Class
Example 2
Example 2-cont
Find the indicated trigonometric function values, if possible.
Find the indicated trigonometric function values, if possible.
a) If tanθ = -5/12 and the terminal side of θ lies in quadrant II, find cosθ
c) If cotθ = 1 and the terminal side of θ lies in quadrant I, find sinθ
b) If cosθ = 40/41 and the terminal side of θ lies in quadrant IV, find tanθ
d) If cosθ = -7/25 and the terminal side of θ lies in quadrant IV, find cosθ
January 27, 2015
Example 3
Evaluate each expression, if possible.
a) sin(-270º) + cos 450º
b) cos(-720º) + tan 720º
c) sin (-450º) + csc 270º
Example 3 - on your own
Evaluate each expression, if possible.
d) sec (-540º) + tan 540º
Ranges of the Trigonometric Functions
-1 ≤ sin θ≤ 1
-1 ≤ cos θ≤ 1
secθ≤ -1 or secθ≥ -1
e) cot (450º) - cos (-450º)
cscθ≤ -1 or cscθ≥ 1
tanθand cotθcan equal any real number
Example 4
Determine whether each statement is possible or not possible.
a) cosθ = 1.001
b) sinθ = √2/10
c) cotθ = -√6/7
d) cscθ = π/2