13-2 · 2009-12-22 · Objective- To measure angles in standard position using degree and radian...
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Objective- To measure angles in standard position using degree and radian measure. y 90° terminal sid e 150° x 0° 180° 270° 360° initial side vertex 150 Draw an angle with the given measure in standard position. Tell which quadrant the terminal side lies. y 240° x 30° Quadrant III Draw an angle with the given measure in standard position. Tell which quadrant the terminal side lies. y 30° 480° x Quadrant II Draw an angle with the given measure in standard position. Tell which quadrant the terminal side lies. y −60° x Quadrant IV Draw an angle with the given measure in standard position. Tell which quadrant the terminal side lies. y 500° −360°= 140° x Quadrant II Draw an angle with the given measure in standard position. Tell which quadrant the terminal side lies. y 500° −360°= 140° Coterminal Angles x Quadrant II −220 ° 500 °, −220 °,140 ° Lesson 13-2 Algebra 2 Slide Show: Teaching Made Easy As Pi, by Mike Mills and James Wenk © 2010
Transcript of 13-2 · 2009-12-22 · Objective- To measure angles in standard position using degree and radian...
Objective- To measure angles in standard position using degree and radian measure.
y 90°terminalsid
e 150°
x0°180°
270°
360°initial sidevertex
150
Draw an angle with the given measure in standard position. Tell which quadrant the terminal side lies.
y240°
x
30°Quadrant III
Draw an angle with the given measure in standard position. Tell which quadrant the terminal side lies.
y30°
480°
x
Quadrant II
Draw an angle with the given measure in standard position. Tell which quadrant the terminal side lies.
y
−60°
x
Quadrant IV
Draw an angle with the given measure in standard position. Tell which quadrant the terminal side lies.
y
500°−360° = 140°
x
Quadrant II
Draw an angle with the given measure in standard position. Tell which quadrant the terminal side lies.
y
500°−360° = 140°
Coterminal Angles
x
Quadrant II
−220°
g500°,−220°,140°
Lesson 13-2
Algebra 2 Slide Show: Teaching Made Easy As Pi, by Mike Mills and James Wenk © 2010
Radian Measure
Another way to measure angles.
y
rr
x1 radian
360° = 2π radians180° = π radians
r x
y
θ(x, y)
rx
r = x2 + y2
Six Trigonometric Functions
y
θ(x, y)sin θ = y
rr
θ x
csc θ = ry
θ rxcos θ =
r
tan θ = yx
sec θ =x
cot θ = xy
Evaluate the six trigonometric functions.
y
θ(-4, 3) sin θ = 3
5
r
cos θ = − 45
tan θ = − 34
csc θ = 53
x
sec θ = − 54
cot θ = − 43
5r =
y
If the terminal side of θŹlies on a axis, then θŹis a quadrantal angle.
x0θ = °
(r, 0)
0x ry==
y
(0, r)0x
y r=
If the terminal side of θŹlies on a axis, then θŹis a quadrantal angle.
x90θ = °
y r=
Lesson 13-2 (cont.)
Algebra 2 Slide Show: Teaching Made Easy As Pi, by Mike Mills and James Wenk © 2010
y
If the terminal side of θŹlies on a axis, then θŹis a quadrantal angle.
x180θ = °(-r, 0)
0x ry= −=
y
If the terminal side of θŹlies on a axis, then θŹis a quadrantal angle.
x
(0, -r)
θ = 270°
x = 0y = −r
Evaluate the six trigonometric functions of
sin θ = cos θ =
θ = 90°x = 0, y = r
=yy= 1y
rxr=
0r= 0
tan θ = csc θ =
sec θ = cot θ =
=y0= undefined
= r0
= undefined
yxrx
ry=
rr= 1
=0y= 0
xy
Reference Angle
x
y
θ
θ '
x
Reference Angle- is the acute angle formed by the terminal side of and the x-axis.
θ '
θ
1. 310°
2. 170°
Find the reference θ ' for each angle θ.
4. 2π3
5. 6π5
θ ' = 360° − 310°θ ' = 50° θ ' = π −
2π3=π3
3. 200°
5
6. 7π4
θ ' = 180° −170°θ ' = 10°
θ ' = 200° −180°θ ' = 20°
θ ' =6π5−π =
π5
θ ' = 2π −7π4=π4
1. Evaluate cos225°
2. Evaluate tan120°
′θ = 225° −180°= 45° Quadrant III
−2
2
′θ 180° 120° 60° Q d II
3. Evaluate sin11π6
′θ = 180° −120° = 60° Quadrant II
− 3
′θ = 2π − 11π6
=π6
Quadrant IV
−12
Lesson 13-2 (cont.)
Algebra 2 Slide Show: Teaching Made Easy As Pi, by Mike Mills and James Wenk © 2010
