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Unformatted text preview: If GA” 45!: PRACTICE PROBLEMS FOR THE FINAL, MATH 3 PRECALU ULUS, 1. Use your calculator to evaluate the following expressions. Rounci to the nearest hundredth1
if necessary. (a) ten 35 (b) cot 35" (6) sec 5% (cl) tan 45° —— tan(—%)
(B) 62 (f) 1031001! 2)) (s) logz 5 (M10315 3
2. Use the reference angle principle to get the exact value of the following expressions:
(3.) sec 135° (1)) cot 120” (c) sin(—§)
3. Graph the following functions.
(a) ﬁx) = tan“($) (b) f(3) = arctanm *1 (1)) HI) = 31660603 1) 4. Graph the function f(a:). = — sin(1r2 + 7r) after ﬁnding the amplitude, period, phase shift and
main cycle._Do the same for 9(2) = 7cos(27r:r:  4) 5 Graph K1?) = %c5c(2:a + %) 6. Give the exact value of sin(arccos £4) by using an appropriate triangle. Do the same for
tan(a.rcsin "T1) and sec(arcta.n 3:). 7. Determine whether the equation for the given graph has the form :1; z Asin Be or y = Acos Hz: (with B > 0) and then ﬁnd the values for A and B.
'7. 8. Find the equation and graph at least 2 cycles of the sine curve 3; 2 Asin(Bs  C) + D with
amplitude 2, phase shift 3'45, period 2 and a vertical shift up by 1. Assume that A > 0. 9. (a) Show that tange — 1 = tam2 :r:si.u2 :I: ~— cos2 x
(b) Show that 1%“ch — Jel— '“ 1«su16I 10. Solve the triangle with sides a = 8,6 = 6 and c = 10.
11. Let 6 be an angle such that sinﬁ = ﬁ and g < 0 < it. Find tan 9, cos 0, sec 3, csc 3, cot 0, sin 20, cos 26, sin(%), sin(%) and H.
12. Use the appropriate formulas to solve the following. (a) Find the exact value of sin 105° using the sum/difference formulas.
(b) Verify the identity cos(:r + 2n) = cos n 13. Give all real solutions (if there are any) to the following equations. (a)lnzz=2 (b)log3m=2logs(z+2)—2 (c)sin:c==—% (d)sinz=3csc:c—2 (e) e2”~5e“—6=D (f) tanzwzi (g)'cosga:—cosz—2=0 f) 14. A 10ft vertical antenna is on the roof of a building. From a point on the ground, the angles
of elevation to the top and the bottom of the antenna are 25° and 21° respectively. Find the
height of the building. 15. A bank offers the following retirement deal: 8% interest, compounded quarterly, invested
money cannot be withdrawn for 30 years. What is the eifective yield of this deal ? How much
do you ham to invest today if you want to have $ 1 million after the 30 years ? 16. Consider the quadratic function defined by f(::) = iii—$2 + a: — 1, dom(f) = [0, 6]
(3.) Find the vertex form of f(a:).
(13) Find the :1:— and y intercepts of f(:r).
(0) Graph the function ﬂit). ((1) Determine the maximum and minimum value for f(a:) on its domain. 1?. Graph the following functions.
(a) 112) = e (b) it») = 1 + r” (c) ft») = 411(3) + 1 (d) 111) = Int: + 1) ~ 1
(9) Km) = (3 +1)(z  1) (1') fix) = (x + 1)($ _ 1)(z + 2)
(E) ﬂat) = (2 + 1X3  1)(== + 2X3  3) {11) ii!) = (I + 1)(='5 — 1)(m + 2)2 18. Give the domains of the following functions: (3)1192): 13(3 + 1) (13) 9(3) =10ga($2 " 1)
19. Find the equation and the graph of the inverse of f(2) = 2:3 + 1. 20 For the rational function f(m) : 3,—— ﬁnd ail intercepts, the equation of all asymptotes _z—2 and the graph. Does the graph intersect its horizontal asymptote ? 21 Find the equation of the quadratic functions with the following graphs: VENOEC '1’...” Uﬂilql ("4) l)
7'“th “—1  9.
22. Give a. reason Why each of the following two graphs cannot represent a. p ynornial function with highest degree term 2.1:“. .
(on 3’ Cb) .
>6 7“ 23. 100 grams of a substance with a halflife of 12 years are released. How much is left after 100
years ? When will only 1 gram be left ? 24. What' is the largest area possible of among all rectangles with a ﬁxed perimeter P. What are
the dimensions and the shape of this largest rectangle? ...
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 Calculus

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