Math 102 PALS
Sample Test 3, Spring 2016 Chpt 8, 9.1-9.3
1.
State the equation of the function f  t  , graphed below.
2
-2
2. Based on your knowledge of cofunctions, state the equation of the function f  t  shown in 1 using a
cosine function.
3. Graph the following functions. Label all of the intercepts, maximums, minimums and asymptotes
if applicable.
 
a. y   sin  t 
b. y  csc  2t   1
3 
4. Alternating current in the United States is modeled with a sinusoidal function whose frequency is 120 Hertz.
What is the period of alternating current in the U.S.?
5. State an equation of the function g  t  shown in the graph below using a tangent function.
2
2
6. State an equation of the function g  t  shown in 5 using a cotangent function.
7. State the amplitude, period, horizontal shift, and vertical shift of the function, then sketch the graph in the
interval indicated. Label all intercepts, maximums, and minimums.
   

y  4cos 3  t    , t  [ , 2 )
3 
2
 
Amplitude: _________ Period: ______ Horizontal Shift: ___________ Vertical Shift: _____________
8. Find the exact value of sin  75o  using a sum or difference formula.
5
4
9. Find the exact value of cos     , given sin    , cos  
,  terminates in quadrant III, and
3
5
 terminates in quadrant IV.
10. Find the exact value of sin  2  , cos  2  , and tan  2  using cos   
8
; tan   0 .
17
8
 
 
 
11. Find the exact value of sin   , cos   , and tan   using cos    ;  in QIII .
17
2
2
2
_______________________________________________________________________________________
Answers: 1) f(t) = 4 sin(t/2); 2) f(t) = 4 cos(/2 - t/2); 4) 1/120 of a sec; 5) g(t) = 3 tan(t/2);
6) g(t) = - 3 cot(t/2 + /2); 7) 4, 2/3, /3, 0; 8) [√2 + √6]/4; 9) - √5/5 – 8/15; 10) cos2x = - 161/(17)2 ,
25
9
34
34
sin2x = -2 (120)/(17) 2 , tan 2x = 240/161; 11) √ , - √ , -5/3
3 a)
3 b)
7)
5
4
3
2
Value
1
0
-1
-2
-3
-4
-5
Angle, Radians

2