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Unformatted text preview: __4__..__...__._______—~_£.;..AA......IA,...M. ' Practice Problems for Midterm 2, Precalculus These problems below serve as a way for you to prepare for the exam, they are not a ' blueprint of the exam; they give you an overview over the tepics that we covered in class as well as examples for the types of questions you’ll encounter. The exam will _ NOT be as long as this. Study these topics before you attend the review session. Answers are also posted for your convenience. 1. Simplify the following expressions.
2. Ita a 900u6
a) ——l~—1—2—~ b) M c) sin4x—2sin2x+1
1+tan or c039 2. Evaluate the following expressions. Round to the nearest hundredth, if necessary. a) sin45°—cos(——7:—) b) 'secZ—secz0 c) cot(—1090°) d) sin (—2—?) 3. Give a table that gives the exact values and the decimal approximations for sinx,
cosx, tanx for x = 0°, x = 30°, x = 45°, x = 60°, and x = 90°. Also give the exact value
of the radian measure of each angle x. 4. How much do you have to invest now if you plan to retire in 40 years with 1
million dollars in the bank, assuming that you can get a constant interest rate of 7%,
compounded continuously? Do the same if the interest rate is 5%. 5. Graph the function f(x) = —23in(2x —2r ), after finding the amplitude, period and phase shift. Do the same for f(x) = écos(7tx+1)q— :2, 6. The point [3, 4) is on the terminal side of an angle 9 in standard position. Draw
6 in a coordinate system and find sine, c056, tan6, secQ, cch and cote. 7. Let 9 be an angle such that
1 .
sin9 = :5 and tam? < 0. Find sinQ , c039 , secQ , (:ch & cote. _ 8. From a point on the ground level you measure the angle of elevation to the top of
a mountain to be 38°. Then you walk 200 yards farther away from the mountain and find that the angle of elevation is now 20°. Find the height of the mountain.
Round your answer to the nearest yard. 9. Prove the following identities: . , sianecQ
a) (1cosoc)(l+ c0305) = tanasmacosoc b) ——~——m =1
 . tanB
{31105 + tan
c) tanartanﬁ = ————ﬁ
cota + cotﬁ 10. The intensity I of light penetrating water decreases exponentially as a function
of depth d. The intensity at a depth of 50 ft. is 1/3 of that at the surface. a) What is the decay rate for intensity as a function of depth in the scenario? b] Find the depth where the intensity is 100 W/ft2 given that the intensity at the
surface is 500 W/ftz. c) What is the light intensity at 100 ft? 11. Use the reference angle principle to get the exact value of the following
expressions: a) 003(135") b) csc(150°) c) tan(450°) d) sin(—210°) e) cot(—405°) 12. What is the angular speed of the little hand in a clock?
13. What is the radian measure of 312°? What is the degree measure of 5? 14. Order the following number in increasing order: sin50, 5, sin5, c0550. 15. Determine whether the equation for the given graph has the form
y = A sian _or y = Acosﬁg (with B > 0) and then find the value for A and B. a) x h) 16. Give a possible equation for this czurve as a sine function and as a cosine
function. " * 17. Graph at least two cycles of coine graph with amplitude 2, phase shift 1/2, period
2. Assume that A>0, B>0. 18. Solve the following equations: a) iog2(x— 3)+ log2(x —4) =1 b) log5(3x + 7) = 2— log5(x — 5) . c) 3"—24(3"‘)=10. d) 29*” =16 e) 111(lnx)=1 ...
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 Winter '08
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 Calculus

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