Download Trig Units 10 and 11 Quest Practice

Trig Units Test Practice
Name______________________________
Station 1 Solving Equations (1st and 2nd Degree)
1) Solve, algebraically, for the exact values of  in the interval 0    360 : 2 cos  5 3  4 3
2) Solve, algebraically, for the exact values of  in the interval 0    2 :
3 tan   4  4 tan   5
3) Solve for  , to the nearest tenth of a degree, in the interval 0    360 : 3 sec   12 
(only an algebraic solution will be accepted)
3
8 sec   4
4

4) Solve, algebraically, for the exact values of  in the interval 0    360 : 5 cos 2   1  3 1  cos 2 
5) Solve for  , to the nearest minute, in the interval 0    360 : 3 tan 2   5 tan   2

Trig Units Test Practice
Name______________________________
Station 2 Pythagorean and Double Angle identities
1) Write each expression as a single function or constant.
a. 1  cos 2 
b. (sin  )(csc  )
c.
csc x
sec x
2) Solve the equation in the interval 0    360 : 3 sin   3  2 cos 2 
3) Solve the equation in the interval 0    360 : 4 cos 2   4 cos 2  1
d. sin 2 x  cot 2 x  cos 2 x
Trig Units Test Practice
Name______________________________
Station 3 Formula sheet identities
7
3
and cos y  and x and y are positive acute angles, find
25
5
a. sin( x  y )
b) tan( x  y )
1) If sin x 
2) Camilla will use her knowledge of trigonometry to compute the exact value of sin 105 .
a. What combination of angles can she use?
b. What is the exact value of sin 105 ?
3) a. Use the half-angle formula for sine to find the exact value of sin 15 .
b. Use your answer to part a to approximate sin 15 to the nearest thousandth.
c. Use your calculator to find sin 15 . Does your answer agree with part a?
Trig Units Test Practice
Name______________________________
Station 4 Graphs and inverse functions
1) Determine the amplitude, shift, period, frequency, and range for the sin curves below. Then write a possible
equation.
a)
amplitude = _________________
vertical shift = _______________
frequency = _________________
period = ____________________
phase shift = _________________
range = _____________________
b)
equation: _______________________________
amplitude = _________________
vertical shift = _______________
frequency = _________________
period = ____________________
phase shift = _________________
range = _____________________
equation: _______________________________
2) Determine the amplitude, shift, period and frequency for the cos curve: y  2 cos3 ( x  0.5)  4
amplitude = _________________
vertical shift = _______________
frequency = _________________
period = ____________________
phase shift = _________________
range = ____________________
3) Multiple Choice: Which expression has the same value as sin arccos 1 ?
3
4
a) cos 
b) csc
c) sec
d) sin 0
2
3
4) What is the domain for y  arcsin x ?
Trig Units Test Practice
Name______________________________
Station 5 applications using trig laws
1) How many distinct triangles can be formed if
°,
and
?
2) The accompanying diagram shows the approximate linear distances traveled by a sailboat during a race.
The sailboat started at point S, traveled to points E and A, respectively, and ended at point S. Based on the
measures shown in the diagram, find the distance from point A to point S to the nearest mile.
3) In Triangle PQR, angle P = 60°, q = 5, r = 8. What is the length of p, to the nearest tenth?
4) A farmer has a triangular field with sides of length 240 feet, 300 feet, and 360 feet. One bag of fertilizer
covers 6,000 square feet. Approximately how many bags of fertilizer does he need to cover the field? (He
can only buy whole bags.)
5) Two forces of 26 and 32 pounds act on a body at an angle of 48°. Find the magnitude of the resultant of
these forces to the nearest hundredth of a pound.