find all 6 trig ratios from the given information. 1. 2. sinθ = 8/133. cotθ = 5 9 15
TRANSCRIPT
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Find all 6 trig ratios from the given information.1.
2. sinθ = 8/13 3. cotθ = 5
Warm Up May 5th
9
15
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Trig on a Coordinate Plane & Angles
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An angle is formed by the rotation of a ray about its endpoint.
The starting position is the initial side and the position after rotation is the terminal side.
A reference angle is the acute angle formed by the terminal side of an angle in standard position (when it’s vertex is at the origin) and the x-axis.
Trig on a Coordinate Plane
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Let (6, 8) be a point on the terminal side of . Find all six trig ratios.
Examples
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Let (-5, -12) be a point on the terminal side of . Find all six trig ratios.
Examples (cont.)
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Find the values of the 6 trig functions of . Examples (cont.)
IVquadrant in lies and 5
2tan
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Degrees are based on fractional parts of a circular revolution.
Degrees
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Radian measure compares the length of an arc that a central angle cuts off to the radius of the circle.
Radians
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To convert degrees to radians:60° -120°
To convert radians to degrees:(7/12)π
Degree & Radian Conversions
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Convert degrees to radians and radians to degrees.
-45º 210º 684º
Conversion Practice
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AnglesPositive Negative Wrapping
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Determine the quadrant in which the angle lies and sketch the angle in standard position. Then state the reference angle.
1) 100°
2) -290°
3) 520°
4) 9π/55) -3π/76) 10π/37) -2
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Angles in standard position whose terminal sides coincide are called coterminal angles.
Determine two coterminal angles (one negative and one positive) for each given angle.1) 140○
2) 3π/7
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Warm Up May 6th Write down the first 10 multiples of the following:1. 30:2. 45:3. 1/6:4. 1/4:5. With a hypotenuse of 1, find the legs.
30○
60○
45○
45○
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Homework Questions?
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The Unit Circle:
a circle with radius 1 and center at the
origin
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30 Degree Reference Angle
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60 Degree Reference Angle
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45 Degree Reference Angle
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Don’t Forget the Radians!
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Using The Unit CircleFind the point on the unit circle that corresponds to the angle.1) 120○ 2) 225○ 3) 330 ○
4) 5) 6) 6
53
2
3
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Using The Unit Circle – tougher Find the point on the unit circle that corresponds to the angle.1) -210○ 2) 675○ 3) -540 ○
4) 5) 6) 3
5
6
232
11
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What does this have to do with Trig?
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1. Sin30
2. Cos90
3. Sin135
4. Cos120
5. Sin 180
6. Cos225
7. Sin240
8. Cos270
9. Sin315
10. Cos330
Unit Circle Practice
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1. Sin30
2. Cos90
3. Sin135
4. Cos120
5. Sin 180
6. Cos225
7. Sin240
8. Cos270
9. Sin315
10. Cos330
Unit Circle Practice - tougher
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Other Trig Functions and their relationship to sine/cosine
sincsc
cossec
tansin
coscot
cos
sintan
1
1
1or
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More Unit Circle PracticeEvaluate each of the following.1. tan(240○) 2. csc(225○)
3) cot(2π/3) 4) sec(π/4)
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A ton of practice…