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Sec 2.1 Trigonometric Functions of Acute Angles October 1, 2012
Sec 2.1 Trigonometric Functions
of Acute Angles
October 1, 2012
Warm – Up (10/1)
B
A C
(x,y)y (opposite side)
r
x(adjacent side)
hypotenuse
Right Triangle w/ Respect to Angle A
Right Triangle Based Definitions of Trigonometric FunctionsFor any acute angle A in standard position,
Right Triangle Based Definitions of Trigonometric FunctionsFor any acute angle A in standard position,
I Do ItFind the values of the six trigonometric functions for angle A.
14
19
23
A
We Do It TogetherFind the values of the six trigonometric functions for angle A.
4652
22A
CofunctionsFind the values of the six trigonometric functions for angle A and B.
4652
22A
Conclusions:Cofunctions
B
C A
a
b
c
The sum of the three angles in any triangle is ____.
Angle B and angle A are ____________ angles. (Since angle C = 90°, the sum of angle A + angle B = 180°- 90° = ____.
Reviewing Facts about Right Triangle
Since angles A and B are: complementary & sinA = cosB (A + B = 90°)
The functions sine and cosine are called
COFUNCTIONS!
Cofunctions
Since 90BA
&sinA = cosB
Thus…
Cofunction IdentitiesFor any acute angle A, since
Cofunction IdentitiesFor any acute angle A, since
Cofunction IdentitiesFor any acute angle A, since
I Do ItWrite the following in terms of its cofunctions.
We Do It TogetherWrite the following in terms of its cofunctions.
You Do It TogetherWrite the following in terms of its cofunctions.
HomeworkPg. 68 #7, 9, 11, 13,
15,17, 19, 21
Warm – Up (10/2)Write the following in terms of its cofunctions.
Since angles A and B are: complementary & sinA = cosB (A + B = 90°)
The functions sine and cosine are called
COFUNCTIONS!
Cofunctions
I Do ItFind a value of θ satisfying each equation. Assume that all angles involved are acute angles.
We Do It TogetherFind a value of θ satisfying each equation. Assume that all angles involved are acute angles.
You Do It TogetherFind a value of θ satisfying each equation. Assume that all angles involved are acute angles.
Comparing Function Values of Special Angles
r
A A
r
A
r
Conclusion:As A increases, y increases. Since r is fixed, sinA increases.
r
Ay
A
ry
A
r y
Conclusion:As A increases, x decreases. Since r is fixed, cosA decreases.
r
A x A
r
x
A
r
x
Conclusion:As A increases, y increases and x decreases. Since r is fixed, tanA increases.
r
A x
A
r y
x
A
r
x
yy
I Do ItTell whether each statement is true or false.
TRUE
We Do It TogetherTell whether each statement is true or false.
FALSE
You Do It TogetherTell whether each statement is true or false.
TRUE
You Do It TogetherTell whether each statement is true or false.
FALSE
Homework (10/2)Pg. 69 # 23 – 33 odds
Warm – Up (10/3)Tell whether each statement is true or false.
Trigonometric Function Values of Special Angles
30°- 60°- 90° Triangle:
30°
60°
1
60°
30° 1
x
1
1
60°
1
30°
Trigonometric Function Values of 30°-60°-90° Angles
For 30° angle:
Hypotenuse =Side Opposite =Side Adjacent =
30°
60°
Trigonometric Function Values of 30°-60°-90° Angles
For 60° angle:
Hypotenuse =Side Opposite =Side Adjacent =
1
30°
Trigonometric Function Values of 45°-45°-90° Angles
45°
45°
x
x
1For 45° angle:
Hypotenuse =Side Opposite =Side Adjacent =
Function Values of Special Angles
θ sinθ cosθ
tanθ
cotθ
secθ
cscθ
30°
45°
60°
I Do ItGive the exact trigonometric function value.
We Do It TogetherGive the exact trigonometric function value.
A line makes a 30° angle with the x – axis and crosses through the origin. What is the equation of the line?
We Do It Together
You Do It TogetherA line makes a 45° angle with the x – axis and crosses through the origin. What is the equation of the line?
We Do It Together
You Do It Together
