Homework for Week 6 Math 232 Spring 2002
This homework will not be collected. It is your responsibility to do as many problems as necessary
to understand the material (this includes doing extra problems if you need more practice). We
recommend that you read each section before attempting any exercises. Next week’s quiz will be a
subset of the problems below.
Section 10.1 1, 2, 4, 5, 7, 9, 16, 22, 23, 24, 27, 31, 33, 35, 36, 37, 38, 39, 40.
Section 10.2 2, 5, 7, 8, 9, 10, 12, 14, 17, 20, 22, 24, 25, 29, 32, 40, 46, 49, 55, 56, 57, 62,
67, 72, 73, 75.
Selected Hints and Answers
Caution: The hints and answers below are not necessarily full solutions. Many of them would not
be considered complete on a quiz or test. Answers are not provided for problems whose
answers can be found in the reading or problems whose answers are easy to check
using a calculator.
Section 10.1
2. They’re all equal to cot θ!
7. TYPO: Should say Figure 8.
(a) True; (b) False; (c) True. (All using the fact that opp >adj.)
16. csc 44◦=1
sin 44◦≈1
0.694658 ≈1.439557.
22. csc 30◦=hyp
opp =1
√3/2=2
√3.
23. cot 45◦=adj
opp =√2/2
√2/2= 1. (Note: √2
2=1
√2; use whichever you like best.)
27. TYPO: Should say Figure 12.
If you think of the 30◦angle as θ, then 5 is the “adj” side. Now tan 30◦=opp
5, so
opp = 5 tan30◦= 5( 1
√3) = 5
√3. Also, 5
hyp = cos 30◦, and thus hyp = 5
cos 30◦=5
√3/2=10
√3.
31. tan 63◦=x
10 , so x= 10 tan 63◦≈10(1.96261) = 19.6261.
33. Isosceles means two sides have the same length (in this case 3). Draw the triangle and split
it into two 30–60–90 triangles. Each of these triangles has side lengths 3, 3
2, and 3√3
2(by
multiplying the sides of our favorite 30-60-90 triangle by three). Therefore the area of the
triangle is A=1
2bh =1
2(3√3
2+3√3
2)(3
2) = 9√3
4.
35. sin 32◦=h
400 , so h≈211.97 feet.
36. Suppose xis half of the distance between the stars (so xis the “opposite” side of both
triangles). Then tan 1◦=x
60 , so x≈1.0473; thus the stars are approximately 2x≈2.0946
light years apart.
37. Proof (a): Suppose θis an acute angle. Then: csc θ=hyp
opp (by definition of csc θ)
=1
opp/adj (algebra)
=1
sin θ. (by definition of sin θ)
40. Proof: Suppose aand bare the lengths of the legs of the triangle (with aas the side
“opposite” to θ). Then (sin θ)2+(cos θ)2= ( a
1)2+ ( b
1)2=a2+b2, which by the Pythagorean
Theorem is equal to a2+b2= 12= 1.
