WorksheetsStudy Guide for sections 6.1-6.5 (By Ryan, Trinity, and Josh)
Total questions: 27
Worksheet time: 13mins
Name
Class
Date
1.
Which is the law of sines?
a)
(signA)/a = (signB)/b = (signC)/c
b)
(cosA)/a = (cosB)/b = (cosC)/c
c)
a^2=b^2+c^2-2bc(sinA)
d)
a/(sinA) = b/(sinB) = c/(sinC)
2.
When can you use the law of sines?
a)
On any shape
b)
On right triangles
c)
Any triangle
d)
Non-right triangles
3.
Which is the law of cosines?
a)
a^2=b^2+c^2-2bc(cosA)
b)
(cosA)/a = (cosB)/b = (cosC)/c
c)
a^2=b^2+c^2-2bc(sinA)
d)
a/(sinA) = b/(sinB) = c/(sinC)
4.
To find the magnitude you use
a)
√( V^2 + U^2 )
b)
√( V^2 x 2 + U^2 x 2 )
c)
The sum of V^2 + U^2
d)
The sum of V2 + 2 + U2 + 2
5.
A unit vector is when
a)
V^2 = 1
b)
||v|| = 2
c)
||v|| = 1
d)
U^2 = 1
6.
The dot product of U • V =
a)
U x V
b)
U1V1 + U2V2
c)
U1V2 + U2V1
d)
U + V
7.
DeMoivre’s Theorem is
a)
r^n(cosnθ + isinnθ)
b)
r^2(cosθ - sinθ)
c)
r^2(sinθ - cosθ)
d)
r^n(sinnθ + cosnθ)
8.
To find the degree between two non-zero vectors ( u and v ) you use:
a)
Cosθ = ( U • V ) / ||U|| ||V||
b)
Sinθ = ( U • V ) / ||U|| ||V||
c)
Cosθ = ||U|| ||V|| / ( U • V )
d)
Sinθ = ||U|| ||V|| / ( U • V )
9.
How do you find the absolute value of a+bi?
a)
a^2+b^2
b)
√a^2+b^2
c)
√a^2-b^2
10.
Find side b using the law of Cosines
a)
6.5
b)
8.2
c)
10.9
d)
7.4
11.
What is the area formula when you don’t know any angles?
a)
½ bcsinA
b)
√s(s-a)(s-b)(s-c)
c)
½ bccosA
d)
√s(s+a)(s+b)(s+c)
12.
What formula do you use when trying to find an angle when only given the 3 sides of a triangle?
a)
½ bcsinA
b)
sin(2x)=2sinxcosx
c)
h=bsinA
d)
CosA= (b2+c2-a2)/(2bc)
13.
Which is an area formula?
a)
a^2=b^2+c^2-2bc(cosA)
b)
½bcsinA
c)
a/(sinA) = b/(sinB) = c/(sinC)
d)
½bccosA
14.
Find the value of x
a)
22.5
b)
38.2
c)
29.6
d)
33.9
15.
Find the value of x
a)
29.68
b)
55.9
c)
42.5
d)
33.95
16.
Find angle B98.6
a)
104.1
b)
36.3
c)
78.7
d)
78.7
17.
Find angle A
a)
28.5
b)
34.7
c)
31.4
d)
36.9
18.
Solve for a
a)
15.7
b)
18.0
c)
13.3
d)
20.1
19.
In the terms of the form, a+bi, how would you write a as a trigonometric function?
a)
Rsinθ
b)
Lcosθ
c)
Rcosθ
d)
Lsinθ
20.
State the number of triangles possible: m∠B = 95°, b = 24, a = 5
a)
1
b)
2
c)
0
21.
State the number of possible triangles:m∠B = 35°, a = 24, b = 6
a)
1
b)
2
c)
0
22.
State the number of possible triangles:m∠A = 29°, c = 18, a = 17
a)
1
b)
2
c)
0
23.
A triangle has two sides with lengths of 63 and 75. The measure of the angle opposite the side with a length of 75 is 22°. Solve the rest of the triangle. (Make up numbers)
a)
∠12.6, ∠55.5, 89.2
b)
∠18.3, ∠139.7, 129.48
c)
∠30.6, ∠44.5, 98.4
24.
Find the length of CB
a)
4m
b)
8.3m
c)
9.5m
d)
6.3m
25.
a)
3.8
b)
12.3
c)
2.45
d)
6.78
26.
Find the length of side B
a)
8.3
b)
9.8
c)
10.5
d)
7
27.
a)
6.2
b)
3.7
c)
8.9
d)
6
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