Exercises
UF Calculus Set 2
1.
(a) Express in radians: 600
◦
(b) Express in degrees:

7
π
12
2.
(a) If a circle has radius 8 cm, find the length of the arc subtended by a central angle of
120
◦
.
Hint: be sure to convert to radians.
(b) Find the area of the sector in part (a).
3. Draw in standard position the angle whose measure is given:
(a)

540
◦
(b)
10
π
3
radians
4. Find the six trigonometric ratios (if possible) for angle
θ
with radian measure:
(a)

5
π
2
(b)
11
π
6
5. If
sec
θ
=

3
2
,
π < θ <
3
π
2
, find the remaining trigonometric ratios.
6. In a right triangle, one angle has measure 38
◦
. Find the length of the side opposite that angle
(correct to four decimal places) if the hypotenuse of the triangle is 16 in.
7. Indicate whether the following statements are true or false. Use the addition and subtraction
formulas stated below to verify your answers.
sin(
x
±
y
) = sin(
x
) cos(
y
)
±
cos(
x
) sin(
y
)
cos(
x
±
y
) = cos(
x
) cos(
y
)
∓
sin(
x
) sin(
y
)
(a)
sin(
π
2
+
x
) = cos(
x
)
.
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 Spring '08
 ALL
 Calculus, Geometry, Trigonometry, Sin, Cos, Radian, Grad

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