Law Of Cosines

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1. (A) -0.7265
2. (C) Side-Angle-Side; law of cosines
3. (C) ellipse
4. (B) f(x) = 3 – cosx
5. (B) There are infinitely many solutions. The solutions are (2t + 1, 4,
t) for all real numbers t.
6. (D) r = 1 – 2sinθ
7. (A) sum of geometric sequence; sum = 6.4416
8. (B) arithmetic sequence; 471
9. a. 300°
b. 132°
10. a. -√ 2
b. -1/√3
11. a. 2π/6
b. π/6
12. x = 90°, 210°, 270°, 330°
13. a. π
b. 2π/3

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14. a. (-√3, 1)
b. (6√ 2, 7π/4)
15. a. Parabola opens to the right
b. vertex : (-2, 3)
c. focus : (0, 3)
16. a. x + y = 2000
52x + 38y = 86780
b. x = 770, y = 1230
c. Out of the total 2000 tickets bought for the amusement park,
770 tickets rating $52/ticket for adults and 1230 tickets rating $38/ticket
for children were sold amounting to total $86780.
17. We will use the definition of sine of angle i.e.,
sin(A) = Perpendicular
Hypotenuse
sin(73°) = h
15
h = 0.9563 x 15
h = 14.34 ft
Yes, the contractor will be able to reach a window that is 14 feet
above ground level
18. a. Comparing with the standard equation : ( x−h)2
a2 + ( y−k)2
b2 = 1
Since b>a as 7>5

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The semi-Major axis of this plot of the given equation is
vertical.
b. We know-
c2 = b2 – a2
c2 = 49 – 25
c = 2√6, -2√ 6
Coordinates of Foci : (5, 3.899), (5, -5.899) or (5, 2 √6 - 1), (5, -
2√6 - 1)
19. cosθ = 12/13
sinθ = (1 – cos2θ)1/2
= (1 – 144/169)1/2
sinθ = ±5/13
Since θ lies in IV quadrant, we have to consider the negative
value only
So, sinθ = -5/13