Download Extending Trigonometry and Radian Measure

Name _______________________________
Advanced Algebra
CHAPTERS 12 & 13
Period ______ Date ___________________
TRIGONOMETRY
Extending Trigonometry and Radian Measure
DRAWING ANGLES Draw an angle with the given measure in standard position. Give the
measure of its reference angle.
6. 110°
7. −10°
9. −900°
23.
40°
25.
−260°
𝟐𝟕.
𝜋
9
𝟐𝟗. 5𝜋
DRAWING ANGLES Convert the radian measure to degrees. Then draw an angle with the
given measure in standard position. Give the measure of its reference angle.
5𝜋
5𝜋
𝟏𝟏.
𝟏𝟐. −
18
3
FINDING ARC LENGTH AND AREA Find both the arc length and the area of a sector with the
given radius r and central angle θ. Expresss your answers both in exact form (in terms of π)
and as a decimal rounded to the nearest hundredth. Give units of measure.
𝜋
34. 𝑟 = 15 cm; 𝜃 = 45°
35. 𝑟 = 12 ft; 𝜃 = 150°
32. 𝑟 = 4 in; 𝜃 = 6
SEE OTHER SIDE
Question #53 is only for GATE:
Advanced Algebra
KEY
CHAPTERS 12 & 13
TRIGONOMETRY
Extending Trigonometry and Radian Measure
DRAWING ANGLES Draw an angle with the given measure in standard position. Give the
measure of its reference angle.
6. 110°
7. −10°
9. −900°
Reference angle: 𝟏𝟎°
Reference angle: 𝟕𝟎°
23.
24.
40°
𝟐𝝅
𝟗
𝟐𝟕.
315°
𝟕𝝅
𝟒
𝜋
9
Reference angle: 𝟎°
𝟐𝟗. 4𝜋
𝟐𝟎°
𝟕𝟐𝟎°
DRAWING ANGLES Convert the radian measure to degrees. Then draw an angle with the
given measure in standard position. Give the measure of its reference angle.
5𝜋
5𝜋
𝟏𝟏.
𝟏𝟐. −
18
3
𝟓𝟎°
Reference angle: 𝟓𝟎°
−𝟑𝟎𝟎°
Reference angle: 𝟔𝟎°
FINDING ARC LENGTH AND AREA Find both the arc length and the area of a sector with the
given radius r and central angle θ. Expresss your answers both in exact form (in terms of π)
and as a decimal rounded to the nearest hundredth. Give units of measure.
𝜋
34. 𝑟 = 15 cm; 𝜃 = 45°
35. 𝑟 = 12 ft; 𝜃 = 150°
32. 𝑟 = 4 in; 𝜃 = 6
𝟐𝝅
𝟏𝟓𝝅
𝒔 = 𝟏𝟎𝝅 ≈ 𝟑𝟏. 𝟒𝟐 𝐟𝐭
𝒔=
≈ 𝟐. 𝟎𝟗 𝐢𝐧
𝒔=
≈ 𝟏𝟏. 𝟕𝟖 𝐜𝐦
𝑨 = 𝟔𝟎𝝅 ≈ 𝟏𝟖𝟖. 𝟓𝟎 𝐟𝐭 𝟐
𝟑
𝟒
𝟒𝝅
𝟐𝟐𝟓𝝅
𝑨=
≈ 𝟒. 𝟏𝟗 𝐢𝐧𝟐
𝑨=
≈ 𝟖𝟖. 𝟑𝟔 𝐜𝐦𝟐
𝟑
𝟖
Question #53 is only for GATE:
𝝅
b) Each step has a central angle of 𝟖 radians and there are 16 steps, so the total rotation
𝝅
is 𝟏𝟔 × 𝟖 = 𝟐𝝅 radians, or what is the same 360°