Test 7: Trig angle formulas

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MQ6 TEST 7B  (answers below)                                                                                     Mr. Gary Jaye

INSTRUCTIONS: 1. Express all answers in simplest form , SHOW ALL WORK, and box answers.
                                    2. NO graphing calculators     3. Use pen (except for graphs)

1. In a-j, fill in all the answers. [4, 3, 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 in
   terms of s, r, and q  is:		 g. equals: h. The change of base formula is:
i. The transformation that maps the graph of y = bx onto     the graph of is: j. In terms of logbA, logb(1/A) equals:

 

 

 

 

 

 

 

 

 

 

 

2. Fill in the answer. [3, 3, 3 for 1st three wrong]
In a-c, apply the Law of Sines or the Law of Cosines correctly to triangle ABC.
a. In terms of triangle ABC, the Law of Sines is:
b. In terms of triangle ABC,
     a2 = 		c. In terms of triangle ABC,
     cos A =
In d and e, do NOT solve. Just state the number of solutions for q in the interval 0° £ q < 360°.
d. tan25q = 1; number of solutions is: e. tan(q /2) = - 1; number of solutions is:

 

 

 

 

 

 

 

 

3. Express as a function of sine, cosine, or tangent. [3, 3, 3 for 1st 3 wrong]
a. cosA cosB - sinA sinB b. sinA cosB - cosA sinB
c.      2tan4x     
       1 - tan24x                 		d. 1 - 2sin26x e. sin22x - cos22x

 

 

 

 

 

4. Use angle formulas- - NOT a calculator- - to evaluate the expression EXACTLY. SHOW WORK
     and SKETCH.
a. tan(-75°)      [10]

 

 

 

 
b. sin2q , sinq = , p /2 < q < p         [10]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5. Solve for q in the interval 0° £ q < 360° to nearest tenth. SHOW WORK and SKETCH q .
a. cos 2q =     [12]

 

 

 
b. cos2q + 3sinq + 1 = 0         [12]

 

 

 

 
c. sin2q + 5sinq + 2 = 0      [14]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6. Evaluate the expression EXACTLY--do NOT use a calculator (it won’t help). SHOW WORK and
     SKETCH.      [13]
cos(157.5° )

 

 

 

 

 

 

 

 

 

 

 


Extra credit: Evaluate the expression and show work. Only an algebraic solution will be accepted.
sin[Sin-1(-12/13) + Tan-1(-3/4)]

 

 

 

 

 

 

 

 

 

 

 

 

ANSWERS:  1. See question 1 from Test 6.    2a. sin A/a = sin B/b = sin C/c     2b. a2 = b2 + c2 - 2bccos A
2c.    (b2 + c2 -  a2)/(2bc)     2d.    20    2e. 1    3a. cos(A + B)    3b. sin(A - B)     3c. tan 8x    3d. cos 12x
3e. -cos 4x    4a. -2 - Ö3     4b. -(3Ö7)/8     5a.  2q Î {150°, 210°, 510°, 570°}, therefore
q Î {75°, 105°, 255°, 285°}     5b. {210°, 330°}     5c. Use quadratic formula: {206°, 334°}
6. -Ö[2 + Ö2]/2     Extra credit: -63/65    

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