Section 22-1: Radians and Degrees
Learning Outcome 1
Find the arc length intercepted on the circumference of a circle by a central angle of
of the circle is 32 centimeters.
s = θr
3π
s=
(32)
8
s = 3π(4)
s = 12π
s = 37.7 centimeters
3π
8
if the radius
Formula for arc length.
Multiply.
Round to tenths.
Learning Outcome 2
Find the area of a sector that has a central angle of 1.7 rad and a radius of 4.8 cm.
1
A = θr 2
Substitute values.
2
A = 0.5(1.7)(4.8)2
Square, then multiply.
2
A = 19.58 cm
(rounded)
Learning Outcome 3
Change 196° to radians and round to the nearest thousandth.
196° ×
π
180°
= 3.421 rad
Learning Outcome 4
3π
radians in degree measure and round to the nearest tenth of a degree.
Write
8
3π rad 180°
×
= 67.5°
8
π rad
Section 22-2: Trigonometric Functions
Learning Outcome 1
Find the sine, cosine, and tangent of angle A in the figure. Round to the nearest ten-thousandth.
11.31
= 0.6283
18
14
cos A =
= 0.7778
18
11.31
tan A =
= 0.8079
14
sin A =
Learning Outcome 2
Find the cosecant, secant, and cotangent of the given triangle. Round to ten-thousandths.
csc A =
sec A =
18
= 1.5915
11.31
18
= 1.2857
14
14
cot A =
= 1.2378
11.31
Section 22-3: Using a Calculator to Find Trigonometric Values
Learning Outcome 1
Use a calculator to find the following: sin 40°, cos 140°, tan 285°
Set calculator in degree mode.
Use a calculator to find the following: sin
3π
, cos 1.8, tan 1.3
4
Set calculator in radian mode.
Learning Outcome 2
Find the value of x in degrees. Sin x = 0.4226182617
Learning Outcome 3
Use your calculator and your knowledge of reciprocal functions to find the following:
π
(a) sec 45° (b) csc 60° (c) cot 1.2 (d) csc
6
Learning Outcome 4
Use your knowledge of cofunctions to find the following:
(a) cotangent 80° (b) sine 20° (c) cosecant 70°
(a) To find the cotangent of 80°, find the tangent of 90° − 80°, or 10°.
tan 10° = 0.176326981
thus, cot 80° = 0.176326981
(b) To find sine 20° using cofunctions, find cosine (90° − 20°) = cos (70°).
cos 70° = 0.342020143
You can check by finding sin 20° directly.
sin 20° = 0.342020143
(c) To find cosecant 70°, find the secant of (90° − 70°) or 20°. But, to find sec 20°, one must use the
knowledge of reciprocal functions. The reciprocal function of the secant is cosine.