how do we convert angle measures between degrees and radians?
DESCRIPTION
You can use reference angles and Quadrant I of the unit circle to determine the values of trigonometric functions. Trigonometric Functions and Reference AnglesTRANSCRIPT
Holt McDougal Algebra 2
The Unit CircleThe Unit Circle
Holt Algebra 2Holt McDougal Algebra 2
• How do we convert angle measures between degrees and radians?
• How do we find the values of trigonometric functions on the unit circle?
Holt McDougal Algebra 2
The Unit Circle
You can use reference angles and Quadrant I of the unit circle to determine the values of trigonometric functions.
Trigonometric Functions and Reference Angles
Holt McDougal Algebra 2
The Unit Circle
The diagram shows how the signs of the trigonometric functions depend on the quadrant containing the terminal side of θ in standard position.
AllStudents
Take Calculus
Holt McDougal Algebra 2
The Unit Circle
sin
cos
tan
0 30 54 60 90
20
1
0
21
23
33
22
22
1
23
21
3
24
0
und.
0 6 4 3 2radian
0 21 1
Holt McDougal Algebra 2
The Unit CircleUsing Reference Angles to Evaluate Trigonometric Functions
Use a reference angle to find the exact value of the sine, cosine, and tangent of each angle.
Step 1 Find the reference angle.
o330 1.330360 o30Step 2 Find the sin, cos, and tan of the
reference angle. Step 3 Adjust the signs, if needed.
AllStudents
Take Calculus
21330sin o
23330cos o
33330tan o
Holt McDougal Algebra 2
The Unit CircleUsing Reference Angles to Evaluate Trigonometric Functions
Use a reference angle to find the exact value of the sine, cosine, and tangent of each angle.
Step 1 Find the reference angle.
o270 2.
270360 o90Step 2 Find the sin, cos, and tan of the
reference angle. Step 3 Adjust the signs, if needed.
AllStudents
Take Calculus
270°
tan 90° = und.
sin 90° = 1cos 90° = 0
1270sin o
0270cos o
und.270tan o
Holt McDougal Algebra 2
The Unit CircleUsing Reference Angles to Evaluate Trigonometric Functions
Use a reference angle to find the exact value of the sine, cosine, and tangent of each angle.
Step 1 Find the reference angle.6
11 3.
6112
6
Step 2 Find the sin, cos, and tan of the reference angle. Step 3 Adjust the signs, if needed.
AllStudents
Take Calculus
21
6sin
23
6cos
33
6tan
21
611sin
23
611cos
33
611tan
Holt McDougal Algebra 2
The Unit CircleUsing Reference Angles to Evaluate Trigonometric Functions
Use a reference angle to find the exact value of the sine, cosine, and tangent of each angle.
Step 1 Find the reference angle.3
4 4.
34
3
Step 2 Find the sin, cos, and tan of the reference angle. Step 3 Adjust the signs, if needed.
AllStudents
Take Calculus
23
3sin
21
3cos
33
tan
34
23
34sin
21
34cos
33
4tan
Holt McDougal Algebra 2
The Unit CircleIf you know the measure of a central angle of a circle, you can determine the length s of the arc intercepted by the angle.
rs
Holt McDougal Algebra 2
The Unit CircleAutomobile Application
5. A tire of a car makes 653 complete rotations in 1 min. The diameter of the tire is 0.65 m. To the nearest meter, how far does the car travel in 1 s?Step 1 Find the radius of the tire.
Step 2 Find the angle θ in radian through which the tire rotates in 1 second.
The radius is of the diameter.
1 rotation = 2.
min 1653
12
Change to seconds sec 06
min 1
sec 30653
30
sec 30653m 325. 2.22rs m/sec
Holt McDougal Algebra 2
The Unit CircleAutomobile Application
6. An minute hand on Big Ben’s Clock Tower in London is 14 ft long. To the nearest tenth of a foot, how far does the tip of the minute hand travel in 1 minute?Step 1 Find the radius of the clock.Step 2 Find the angle θ in radian through which the hour hand rotates in 1 minute.
1 hour = 2.
hour 12
Change to minutesmin 06hour 1
min 30
30
min 30ft 41 5.1rs ft/min
r =14
Holt McDougal Algebra 2
The Unit Circle
Lesson 10.3 Practice B