October 2
Do Now: College Prep
p. 691
6a.
8a.
b.
b.
c.
c.
d.
d.
e.
e.
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10a.
16.
b.
18.
c.
20.
d.
e.
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Cofunctions
The Pairs of Cofunctions:
sine and cosine
tangent and cotangent
secant and cosecant
Any trigonometric function of an acute angle is equal to the cofunction of its complement.
ex. sin A = cos B
if A + B = 90
tan θ = cot α
if θ + α = 90
sec S = csc T
if S + T = 90
October 2
Want proof?
Find the value in your calculator and round to the nearest four decimal places.
1) sin 30
cos 60
2) tan 38
cot 52
3) sec 67
csc 23
Examples
1. If sin x = cos (x+20), and x and (x+20) are the measure of two acute angles, find x.
October 2
2. If cot (θ+7) = tan (2 θ+7) and (θ+7) and (2 θ+7) are acute angles, find θ.
3. Express sin 285 as the function of a positive acute angle whose measure is less than 45.
1. Use reference angle rules to express the function as a function of a positive acute angle (check the sign).
2. Use cofunctions (do NOT change the sign).
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4. Express sec 490 as the function of an acute angle whose measure is less than 45.
Express each as a function of an acute angle whose measure is less than 45.
a) cos 110
b) sec 125
c) cos 635
d) tan (­50 )
e) sin (­100 )
October 2
Homework: p. 695 (2 ­ 46e)
Skip 10, 12, 18, 38