## Description

Thank you in advance,

### Unformatted Attachment Preview

1.) Find the length a.
2.) Find the missing side length.
For questions 3 – 4 assume the triangle has the given measurements. Solve for the remaining sides and
angles.
3.) C 100 , a
4.) A
1
1
, b
2
3
, b 17.4, c 19.6
6
For questions 5 – 6 solve for the remaining angles.
5.)
6.)
7.) Viewed from Earth, two stars form and angle of 83.23°. Star A is 33 light-years from Earth, and
Star B is 21 light-years from Earth. Sketch a diagram modeling this situation and find out how
many light-years the stars are away from each other.
Questions 8 – 10 deal with the ambiguous SSA case. For each, find all possible solutions and sketch the
triangle in each case.
8.) A 50 , a 5, b 3
9.) A 50 , a 3, b 5
10.) A 130 , a 1.2, b 3
11 – 14. Solve the given triangles by finding the missing angle and other side lengths.
11.)
12.)
13.)
14.)
Compute the following linear combinations.
15.) 4 1, 7 2 5, 3
16.) 22.2, 19.9 3 0.8, 6.3
17.) Let v1 3, 5 and v2 4, 7 .
(a) Compute v1 and v2
(b) Compute the unit vectors in the direction of v1 and v2 .
(c) Draw and label v1, v2 , and their unit vectors on the axes provided.
18.) Let v1 6, 4 and v2 3, 6 . Compute the following.
(a)
v1 • v2
(b) The angle between v1 and v2 .
(c) The scalar projection of v1 onto v2 .
(d) The projection of v1 onto v2 .
19.) Derive this identity from the sum and difference formulas for cosine:
sin a sin b
1
cos a b cos a b
2
Start with the right-hand side since it is more complex.
Answer:
Calculation
Reason
20.) Use the trigonometric subtraction formula for sine to verify this identity:
sin x cos x
2
Answer:
Calculation
Reason
21.) Find the exact value of each of the following using half-angle formulas:
(a)
7
cos
12
17
tan
12
cot 15
sin 195
Answer:
22.) Rewrite sin4 x so that it involves only the first power of cosine.
Answer:
23.) Prove the identity:
sin 2 x
sin x
Answer:
cos 2 x
cos x
sec x
24.) Prove the identity:
cos x cos y 2 sin x sin y 2 2 2cos x y
Answer:
25.) Solve these equations graphically on the interval 0,2 . Sketch the graph and list the solutions.
(a)
sin x 1 cos x
sin 2x 1 tan x
Answer:
26.) Solve these equations:
(a)
sin x sin x 1
4
4
(b) sin x cos x
(c)
Answer:
3
4
tan2 x 3 tan x 2 0

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