Test 3: Trig graphs and basic trig review

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MQ6 TEST 3A  (answers below)                                                                                        Mr. Gary Jaye

INSTRUCTIONS:   1. NO calculators           2. Label all graphs and axes
                                  3. Express all answers in simplest form and SHOW WORK when requested.

1. In a - g, fill in all the answers. [5, 4, 3 off for first 3 wrong answers]
In #a- c, fill in the three Pythagorean identities.
a. b. c.
In d- e, state the two standard equations of the unit circle, center at origin.
d. e.
f. The definition of radian measure is:
g. If f[g(x)] = x, the transformation that maps the graph of y = f(x) onto the graph of y = g(x) is: h. The transformation that maps the graph of y = a trig bx onto the graph of y = - a trig bx is:


 

 

 

 

 

 

 

2. In a - d, convert to degree measure. [3,3 first two wrong]
a. 7p 
     6		 b. 3p 
      4		 c. 9p 
      2		 d. 5p 
      3
e. In a circle, a central angle of 1.5 radians intercepts 6 cm of arc. Find the length of the radius. Show work. [3]

 

 

 

 

 

 

 

3. Equation of Graph

Amplitude

Frequency

Period
a. y = - 5 sin (2x/3) [2, 1]      
b. y = 4 tan 3x [2, 1]      
c. y = - 2 sec(3x/2) [2, 1]      
d. If the period of graph of y = a sin bx is 4p /3, the frequency of the graph is: [3]

 

 

 

 

 

 

 

4. In a - e, evaluate the expression by sketching. SHOW WORK [3 each]
a. cos p

 

work area for 3a and 3b

 
b. 2 cos 0° - 5 sin 270°

 

  

 
c. tan 315°

 

 d. cos 150°

 

 e. sin 240°

 

 

 

 

 

 

 

 

 

5. Given sinq = - 2/3 and tanq > 0; Find cos q , tan q , sec q by sketching. Must show diagram(s). [10]

 

 

 

 

 

 

 

 

 

 

6a. Sketch graph of y = - 4 cos (x/3) over - 6p / £ x £ 6p . [14]
wpe6.gif (2013 bytes)

 
b. domain:

 

 c. range:

 

 d. a line or point of symmetry:

 

 

 

 

 

 

 

 

 

 

 

 

 

7a. Sketch graph of y = - tan 2x over - p /4 £ x £ 3p /4. [14]
wpe1.gif (2288 bytes)

 
b. domain:

 

 c. range:

 

 d. a line or point of symmetry:

 

 

 

 

 

 

 

 

 

 

 

 

 

8a. Sketch graph of y = 7 csc 3x over - 2p /3 £ x £ 2p /3. [14]
wpe3.gif (2288 bytes)

 
b. domain:

 

 c. range:

 

 d. a line or point of symmetry:

 

 

 

 

 

 

 

 

 

 

 

 

 

ANSWERS: 1a-1c. sin2q + cos2q = 1, tan2q + 1 = sec2q , and cot2q + 1 = csc2q    1d-1e. x2 + y2 = 1,
sin2q + cos2q = 1   1f. |q | = s/r   1g. ry=x   1h. rx-axis    2a. 210°   2b. 135°    2c. 810°   2d. 300°    2e. 4 cm
3a. (5, 2/3, 3p )   3b. (NA, 3, p /3)   3c. (NA, 3/2, 4p /3)   3d. 3/2    4a. - 1   4b. 7   4c. - 1   4d. - Ö 3/2   4e. - Ö 3/2
5. cosq = - Ö 5/3,  tanq = (2Ö 5)/5,   secq = (- 3Ö 5)/5   6b. R   6c. {- 4 £ y £ 4}   6d. y-axis    7b. {x: - cos2x ¹ 0}
7d. origin   8b. {x: 7sin3x ¹ 0}   8c. {y: y £ - 7 OR y ³ 7}   8d. origin, y = p /6, others

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