Course: 112 Precalculus Part 2

Instructor: R. Porter
 
 

Sample Exam 2

( Please note that Prof. Porter Likes to use the graphing calculator and this exam may reflect this fact. Other professors may choose more traditional methods.)

1. a) Find the terminal point P(x,y) on the unit circle determined by t = 2

answer__(-.42,.91)_______________

b) What is the reference number when t = 2?

(to two decimal places)  in Q2 from above. so ref. angle is p-2 =

answer______1.14___________

c) Find the terminal point P(x,y) on the unit circle determined by t = -5p /6

ref angle is p/6  in Q 3 x= -cos(p/6)   y = -sin(p/6)

answer__(-.87,-.50)_______________

d) Find the reference number p/6
 

answer____p/6_____________

2) a) Change -150 degrees to radians.

-150 * (p/180) =-5p/6 

answer________-5p/6_________

b) Determine the exact value of the trig function at the given real number. sec (-150^o)

sec (-150^o) = 1/cos (-150^o)= -1/cos(30^o)=-2/sqr root (3)

answer________-2/sqr root (3)_________

3) Given that sin x = 3/4 and tan x < 0, find remaining trig values:

3=opp   4=hyp   adj= -sqr root(16-9)= -sqr root (7) (in Q2)

cos x = _sqr root (7)/4____________

tan x = __3/sqr root(7)___________

sec x = __4/sqr root(7)___________

csc x = ___4/3__________

cot x = __sqr root (7)/3___________

4) Graph one period of the function f(x) = 3 sin (x/8 - p /8)

Looks like a sin curve moved to the right by pi, with a long period of 16 pi, and an amplitude of 3

5) Find the period, amplitude, phase shift for the function in 4.

Period:_2p/(1/8)=16p_________________

Amplitude:___3____________

Phase Shift:__p____________
 

6) a) Given the data, find an exponential regression.
 

Time	20	25	30
Height	100	110	150

stat>edit:1 edit
L1  L2
20  100
25  110
30  150
stat>>calc:0 ExpReg

answer__See (b)_______________

7) Given the data, come up with an appropriate model y = A sin ( B x + C) + D
 

Year	1979	1980	1981	1982	1983	1984	1985
Profits	55	25	55	85	55	25	55

ampl=85-55=30 so A=30

period= 4 = 2p/B
 so B=p/2

PS= -C/B = 1979-4(494)=3  C= -3B = -3p/2
  so C=-3p/2

Raised up by 55,
  so D = 55

A = ____ B = ____ C = _____ D = _____

8) Graph one period of the function f(x) = 6 tan (3x - p /3)

looks like a regular tangent except the period is shortened by a third.There are asymptotes at p/9, -p/9

9) Give the period and phase shift for the function in 8)

Period:_p/3_________________

Phase Shift:_p/9_____________

10) Find the length of an arc that subtends a central angle of 30 degrees in a circle of radius 15.

s = r q   q = 30p/180=p/6

s = 15 p/6

answer___5p/2_____________
11) Given the data below, draw a scatter plot.
 

Year	1979	1980	1981	1982	1983	1984	1985
Profits	3	4	3	2	3	4	3

stat>edit:1 Edit
L1   L2
79 3
80 4
81 3
82 2
83 3
84 4
85 3
stat plot:1  on
zoom:9 ZoomStat

b) What type of regression would you use to model the situation.

SIN regression has a periodic behaviour

answer__SIN_______________

c) Predict the profits in 1995.

answer_3________________
 

12) Fifteen miles away from the peak of a mountain top an observer notes that the angle of elevation to the top of the mountain is 12 degrees. How high is the mountain?

adj = 15, angle =12, desire opp. Use tan (12) = opp/adj  opp = 3.19

answer____3.19_____________

13) a) Find the terminal point on the unit circle when x = 2/3 and in Quadrant 1?

x=2/3, y = 1-(2/3)^2 from equation of unit circle.

answer__5/9_______________

b) What is the angle corresponding to the terminal point above in degrees?

arccos(2/3) = 48.19

answer___48.19______________

14) An airplane travelling at a speed 400 miles per hour and an altitude of 2 miles begins to descend at an angle of 8 degrees. How long will the plane take to land?

opp = 2, angle = 8 degree hyp desired so sin (8) = 2/hyp hyp = 2/sin(8) = 14.37miles

time = distance/rate = 14.37 / 400 = .036 hours = 2.15 mins = 129.34 seconds.