Sec 2.1 Trigonometric Functions of Acute Angles October 1, 2012.
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Transcript of Sec 2.1 Trigonometric Functions of Acute Angles October 1, 2012.
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,
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 angles A and B are: complementary & sinA = cosB (A + B = 90°)
The functions sine and cosine are called
COFUNCTIONS!
Cofunctions
I Do It
Find a value of θ satisfying each equation. Assume that all angles involved are acute angles.
We Do It Together
Find 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.
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
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
1
For 45° angle:
Hypotenuse =Side Opposite =Side Adjacent =
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?