Trigonometry_2.1_Sept 8 & 9
• 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 A
Sin A =
7
25
Cos A =
24
25
Tan A =
7
24
Csc A =
25
7
Sec A =
25
24
Sin B =
24
25
Cos B =
7
25
Cot A =
24
7
Tan B =
What do you notice?
24
7
Csc B =
25
24
Sec B =
25
7
Cot B =
7
24
C
B
Sin A =
7
25
A
Cos B =
7
25
= 90 ∘
= Cos B
Another way to think of it...
Sin A = Cos ( )
This makes sin & cos cofunctions
1

Trigonometry_2.1_Sept 8 & 9
Function pairs that are complementary (i.e. sum to 90 ∘ ) are called...
___________________ sin θ = cos (90 - θ ) sec θ = csc (90 - θ ) tan θ = cot (90 - θ ) cos csc cot
θ
θ
θ
= sin (90 -
= sec (90 -
= tan (90 -
θ
θ
θ
)
)
)
Cofunctions of Complementary angles are equal.
[try these examples on your calculator] think...sin 36 o = cos (90 - 36 o ) sin θ = cos (90 - θ ) ex: sin 36 o = cos 54 o sec θ = csc (90 - θ ) ex: sec 70 o = csc 20 o tan θ = cot (90 - θ ) ex: cot 11 o = tan 79 o
Ex. II a.) Solve: tan ( α + 30 o ) = cot (7 α - 40 o ) remember... tan A = cot B & A + B = 90 b.) Solve: cos (2 𝜃 − 18 o ) = sin ( 𝜃 + 18 o )
Ans 𝜃 = 30
Ex. I Write in terms of the cofunction: think...
Cos A = Sin ( 90
∘
- A ) cos 41 o = think...
Tan A = Cot ( 90
∘
- A ) tan ( β - 30 o ) =
Trig values for special angles
( You must memorize ): sin cos tan
30 o
45 o
60 o x 2
2
+ y 2
2
= r 2
2
2
2
60°
2
2
60°
2
2
2
60°
1
45°
1
45°
2

Trigonometry_2.1_Sept 8 & 9
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 60 o b.) cot 30°
Ex. IV
9 y w
30° x z
60°
Ex. IV
Find the exact value of each part labeled.
(challenge problem)
9 y w
30° x z
60°
=
= = =
Answers
3