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3) A triangle has an area of 184 in², and two of the sides of the triangle have lengths 30 in and 13 in. Find the angle included by these two sides.
Note: There are two possible answers.
Report each answer accurate to 2 decimal places.
acute angle =??°
obtuse angle =??°
4) A population of rabbits oscillates 33 above and below average during the year, hitting the lowest value in January (t = 0). The average population starts at 850 rabbits and increases by 160 each year. Find an equation for the population, P, in terms of the months since January, t.
P(t)=??
Box 1: Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c
5) Given the equation y=2tan(7x+28)
The period is:??
The horizontal shift is:?? units to the right or left??
6) Given the equation y=6sin((4 pi)/3 x-(32 pi)/3)+3
The amplitude is:??
The period is:??
The horizontal shift is:?? units to the right or left??
The midline is: y =??
7) Find the values of the trigonometric functios of the real number t given that tant=-1.25561 and csct＞0. To be on the safe side, report all answers accurate to 5 decimal places.
Sint=
Cost=
Cott=
Sect=
Csct=
8) Without using a calculator, find the exact value of the expression: 9tan^2(pi/3)+18sec^2(pi/4)
9) For this problem, all answers should be exact. These means use pi and sqrt() where appropriate (no decimal approximations---except for 0.5).
What radian measurement t^** in the interval ［0,2pi］ is coterminal to the real number t=(-33pi)/4?
T^**=??
What is the reference number bar t (in radian measure) for the real number t=(-33pi)/4?
Bar t=??
What is the terminal point determined by the reference number bar t?
P(bar t)=(??,??)
What is the terminal point determined by the coterminal value bar t?
P(t^**)=(??,??)
Finally, what is the terminal point determined by t=(-33pi)/4?
P(t)=(??,??)
10) The equation of the hyperbola that has a center at (5,6), a focus at (0,6), and a vertex at (8,6), is frac((x-C)^2)(A^2)- frac((y-D)^2)(B^2)=1
A=??
B=??
C=??
D=??
11) Write the equation of the ellipse 16x^2+25y^2-96x+50y-231=0 in standard form (x-h)^2/a^2+(y-k)^2/b^2=1
Where:
h=??
k=??
a=??
b=??
# Enter your answer as a number. Examples: 3, -4, 5.5
Enter DNE for Does Not Exist, oo for Infinity.
12) Find an equation for the parabola that has its vertex at the origin and has a focus at the point (0,27).
13) Let bar a = <0,-5,4> and bar b= <1,0.-1>
Find the angle between the vector (in radians)
14) An airplane is heading north at an airspeed of 550 km/hr, but there is a wind blowing from the northwest at 80 km/hr.
The plane will end up flying ?? degrees off course
The plane's speed relative to the ground will be ?? km/hr
15) Given the vector vac u =-5 vec i + 2 vec 1 j, find the magnitude and angle in which the vector points (measured counterclockwise from the positive x-axis, 0 ≤ θ＜2pi)
IIvec uII=??
θ=??
16) Convert the Cartesian coordinate (4,2) to polar coordinates,0≤θ＜2pi, r＞0
r=??
θ=??
17) Solve -5cos^2(x) +4cos(x)+1=0
The smallest non-negative solution is:??
The next smallest non-negative solution is:??
18) Solve 6sin(2x)=2x for the two smallest positive solutions A and B, with A < B
A=??
B=??
Give your answers accurate to at least two decimal places.
19) Evaluate the following expressions. Your answer must be an exact angle in radians and in the interval［o,pi］. Example: Enter pi/6 for pi/6.
(a) cos^(-1)(-1)
(b) cps^(-1)(1)
©cps^(-1)(-1/2)
#Enter your answer as a number (like 5, -3, 2.2) or as a calculation (like 5/3, 2^3, 5+4)
Enter DNE for Does Not Exist, oo for Infinity
Decimal values are not allowed
Trig functions (sin,cos,etc.) are not allowed
20)Let f(x)=1/(-2.6sinx+6.4cosx). Using interval notation, give the range for this function:
Range=??
#Enter your answer using interval notation. Example: [2.1,5.6)
Use U for union to combine intervals. Example: (-oo,2] U [4,oo)
Enter DNE for an empty set, oo for Infinity
Your numbers should be accurate to 4 decimal places.
21) Express -6.3sin(x)+4.4cos(x) in the form ksin(x+φ)
K=
φ=
#φshould be given in radians in the interval -pi<Φ<pi
Report answers accurate to 4 decimal places.
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