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