Trigonometry_2.1_Sept 2 & 3
Sec 2.1 Trig Functions of Acute Angles
• Find trig function values of an acute angle in a
right triangle
• Write functions in terms of their cofunctions
• Solve equations by using cofunction identities
• Review function values of "special" angles
2.1 Trig functions of acute angles
Try this on your own before we start notes!
Suppose ABC is a right triangle with sides a, b, c. Find the unknown side
length and all 6 trig values for angle A and angle B.
b = 24, c = 25
B
Assumptions:
side a is opposite angle A;
side b is opposite angle B;
side c is opposite angle C
C
Sin A =
7
25
Csc A =
25
7
Sin B =
24
25
Csc B =
25
24
Cos A =
24
25
Sec A =
25
24
Cos B =
7
25
Sec B =
25
7
Tan A =
7
24
Cot A =
24
7
Tan B =
24
7
Cot B =
7
24
What do you notice?
A
Sin A =
7
25
Cos B =
= 90∘
B
see next slide
C
7
25
A
Sin A = Cos B
Another way to think of it...
Sin A = Cos (
)
This makes sin & cos cofunctions
1
Trigonometry_2.1_Sept 2 & 3
Function pairs that are complementary (i.e. sum to 90∘) are called...
Ex. I
Write in terms of the cofunction:
think...
___________________
sin θ = cos (90 - θ)
sec θ = csc (90 - θ)
tan θ = cot (90 - θ)
Cos A = Sin (90∘ - A)
cos 41o =
cos θ = sin (90 - θ)
csc θ = sec (90 - θ)
cot θ = tan (90 - θ)
think...
Tan A = Cot (90∘ - A)
Cofunctions of Complementary angles are equal.
[try these examples on your calculator]
Ex. II a.)
think...sin 36o = cos (90 - 36o)
sinθ = cos (90 - θ)
ex: sin 36o = cos 54o
secθ = csc (90 - θ)
ex: sec 70o = csc 20o
tanθ = cot (90 - θ)
ex: cot 11o = tan 79o
Solve: tan (α + 30 ) = cot (7α - 40 )
o
remember...
tan A
tan (β - 30o) =
o
=
cot B
&
A + B = 90
Trig values for special angles
(You must memorize):
sin
cos
x2 + y2 = r2
2
2
tan
30o
2
45o
Solve: cos (2𝜃 − 18o ) = sin (𝜃 + 18o)
2
60°
2
2
2
60o
Ans
𝜃 = 30
60°
60°
2
b.)
2
2
45°
1
45°
1
2
Trigonometry_2.1_Sept 2 & 3
The complete table (You must memorize):
2.1 Assignment:
page 69-71
#'s 5-25 (skip #11) odds, 35-45 odds
(BONUS problem #59)
Ex. III
Give the exact trig value (don't use a calculator.)
a.)
sin 60o
b.)
cot 30°
Ex. IV
Find the exact value of each part labeled.
(challenge problem)
Ex. IV
Find the exact value of each part labeled.
(challenge problem)
9
9
x
60°
30°
60°
30°
w
y
w
y
x
z
z
=
=
=
=
Answers
3