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Mathematics 142 first homework
1.
semi-circle
C
D
A
43◦
B
center
find values for angles A,B,C, & D
The triangle to the right of the center is isosceles, so that A = B and A + B + 43◦ = 180◦
imply that A = B = 67.5◦ .
The triangle to the left of the center is also isosceles. The supplemental angle to the left of
43◦ measures 137◦ , so that C = D = 21.5◦ .
2. A circle has an area of one square centimeter. Calculate the circle’s diameter and
circumference.
s
A = πr2 =⇒ 1 = πr2 =⇒ r =
1
π
√
2
2π
D = 2r = √ and circumference = πD = √ = 2 π
π
π
3. A central angle A intercepts an arclength of s = 780 miles on a circle of radius 4000
miles. Find the measure of the angle A in radians.
A=
s
780
=
= 0.195
r
4000
4. A slice from a circular pie has an acute angle of 40◦ and has a crust with a length of ten
centimeters. Find the area of the pie slice.
r=
10
45
s
=
=
π
A
π
40 · 180
45
A=π
π
2 40
225
=
360
π
√
89
5. Write down the values of the six
trigonometric functions of the angle A:
( sin A, cos A , etc.)
5
A
8
5
sin A = √
89
√
89
csc A =
5
6. Suppose that tan A =
8
cos A = √
89
√
89
sec A =
8
tan A =
5
8
cot A =
8
5
2
5
(a) Draw a right triangle showing the angle A
and side lengths 2 and 5 in the correct positions.
(b) Use the Pythagoras theorem to find
√ the
length of the last side of the triangle. = 29
(It’s OK to leave this as a square root)
(c) Find the
and sin A.
√ values of cos A √
cos A = 5/ 29 and sin = 2/ 29.