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**Unformatted text preview: **Math 119 Test 1
1/27/98 Mike Robertson Name _ - r __ Instructions. No calculators are allowed on this exam. Please answeﬁll questions clearly. Unsupported answers may receive no credit. 1. Provide a brief explanation, or proof, as to why the following statements are TRUE: (a) Each of the six trigonometric functions can be deﬁned in terms of points on the
unit circle. You may refer to what is here for later parts 0 (b) It must be, for any value such that cost % 0, that sect = 005,. ﬂ -0. (c) Given that 0 < a < %, it’s true that sin (a) = sin (7? — a) . 0 (d) For small values of a: (say 0 < :L' < .1) sins: % (1:. (Both are approximately the same. ) 2. Fill in the exact values on the following table: -H- W «=27: as: ' n-I "all!
4
/ >< A A
7;? 3. Graph the following on a Cartesian graph, showing more than one full period. A
9:
v
"w
("N
c-l
V
II -—3 cos (2.1:) (c) f (.13) = — csc (2:1: — 7r) 4
% 4. Plot the following points on a polar graph (and label so I can tell which is which): (3,37"),(1,w), (a), (—23%)- 5. Graph the following two curves in polar coordinates r = 3 — 2cos 8, a limagon
45in (39) , a three petaled rose a
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