Mathematical Investigations III
Name
Mathematical Investigations III
Trigonometry- Modeling the Seas
TRIG. EQUATIONS AND APPLICATIONS
Approximate Solutions
1.
Put your calculator in degree mode. Consider the equation sin(x)  0.2 .
a. Show the approximate location of the b. Use your calculator to find the solution in
two solutions in [0, 360).
the first quadrant, correct to the nearest
tenth of a degree.
c.
Use geometry and your calculator to find
the other solution in [0, 360), again to the
nearest tenth of a degree.
d. List all real solutions. (You will need to use a form that includes something like
360k, k  .)
2.
Leave your calculator in degree mode. Use symmetry, geometry, and what you know about
the unit circle and the graphs of the functions, to find ALL solutions to the nearest tenth of
a degree.
cos(x)  0.7
sin(x)  .8
a.
b.
c.
tan(x)  1.5
d.
sec(x)  4
e.
sin(2x  10)  0.9
f.
x
tan    0.6
2
Trig. 15.1
Rev. S05
Mathematical Investigations III
Name
3.
Change your calculator back to radian mode. Find all solutions to the following
equations to the nearest hundredth of a radian.


sin(x)  0.3
a.
b.
cos  3x    0.3
4

c.
3sec(x)  5  0
d.
tan(2x)  0.8
1

5
 2k . Find the specific
, then x   2k or
2
6
6
solutions given by each of the particular values of k stated below.
a. k = 0
b. k = 3
c. k = –2
4.
Stay in radian mode. If sin(x) 
5.
Find all real solutions in radians. Choose and state the values of k that will give only
those solutions in the interval [0, 2). Use these values to state the actual solutions in the
interval [0, 2).
sin(x)  .4
a.
b.
cos(x)  .6
Trig. 15.2
Rev. S05
Mathematical Investigations III
Name
5.
Continued. Find all solutions in [0, 2).
c.
tan(x)  3
d.
sin(2x)  .25
e.
sin(x  3)  .8
f.
tan(3x)  5
g.
 x
cos    .3
 2
h.
cos(3x  5)  .4
A few applications…
6.
Find an approximate the height of a tree if you are 30 meters from the tree and the angle
of elevation is 23°.
Trig. 15.3
Rev. S05
Mathematical Investigations III
Name
7.
The sides of a rectangle are 3 and 8. Find the angles formed exclusively by the two
diagonals.
8.
The legs of an isosceles triangle are 18 cm long and the angle between them is 58°.
Find the length of the base.
9.
Two roads, Marchant and Barker, meet
at a right angle. Alban intersects
Marchant at a 41° angle at a point that
is .8 miles from the intersection of
Marchant and Barker. How far is the
Marchant-Barker intersection from the
intersection of Alban and Barker?
Alban
Barker
Marchant
Trig. 15.4
Rev. S05