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3.5 The Trig Functions. sine and cosine are only 2 of the trig functions! Here are all 6!. cosecant. sine. , y ≠ 0. cosine. secant. , x ≠ 0. cotangent. tangent. , y ≠ 0. , x ≠ 0. - PowerPoint PPT Presentation
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3.5 The Trig Functions
sine
cosine
cosecantsiny
r
secant
tangent cotangent
cosx
r
tany
x
cscr
y
secr
x
cotx
y
sine and cosine are only 2 of the trig functions!Here are all 6!
, x ≠ 0
, x ≠ 0
, y ≠ 0
, y ≠ 0
Ex 1) The terminal side of an angle θ in standard position passes through (–1, 7). Draw the reference triangle and evaluate the six trig functions of θ.
5 2 r–1
7 r
θ
72 + (–1)2 = r2 50 = r2
7 2 7 2sin
105 2 2
y
r
1 2 2cos
105 2 2
x
r
7tan 7
1
y
x
5 2csc
7
r
y
5 2sec 5 2
1
r
x
1cot
7
x
y
r always (+)
Ex 2) Determine the value of secθ if cosθ = 0.11
1 1sec 9.09
cos 0.11
1csc
sin
1sec
cos
1
cottan
A relationship among the 6 trig functions is they can pair up & make pairs of reciprocal functions. (as always den ≠ 0)
If we know the value of one trig function & the quadrant of θ, we can get the other 5
Ex 3) Angle in standard position, Quadrant IV and 2 2 2
2
2
7 ( 6)
49 36
13
13
x
x
x
x
–67
13cos
7
6sin
7
θx
6 6 13tan
1313
7 7 13sec
1313
13cot
6
7csc
6
13
Ex 4) Suppose that cos θ = 0.42 and
Use the symmetry of the unit circle to find the exact values of the following.
a) cos(–θ)
02
θ–θ
x-value is the sameso cos(–θ) = 0.42
b) cos(θ + π)
θ
+ π
x-value is negativeso cos(θ + π) = –0.42
c) cos(θ + 2π)
θ
+ 2π
right where you started so cos(θ + 2π) = 0.42
Homework
#305 Pg 150 #1, 5, 9, 13, 15, 17, 21, 26, 27, 29, 31, 33, 37, 43, 44, 45, 46