station 1 - Sonoma Valley High School

STATION 1
When a satellite is fired into orbit from a site such as Cape Canaveral, which is not on the equator, it goes into
an orbit that takes it alternately north and south of the equator. Its distance from the equator is
approximately a sinusoidal function of time. Suppose that a satellite is fired into orbit from Cape Canaveral.
Ten minutes after it leaves the Cape, it reaches its farthest distance north of the equator, 4000 kilometers.
When it reaches its farthest distance south of the equator, it is 4000 kilometers south of the equator. The
satellite completes an orbit once every 90 minutes.
a) Sketch a graph that represents the distance from the equator as a function of time where the time is
the number of minutes that have elapsed since liftoff.
b) Write an equation that represents the distance from the equator as a function of time.
c) Predict the distance of the satellite from the equator one hour after liftoff.
d) Calculate the distance of Cape Canaveral from the equator by finding the distance at the time of liftoff.
(compare this to the actual distance of 3165 km to see if the model gives accurate answers)
e) Calculate the first four times that the satellite will be the same distance away from the equator as San
Francisco (2551 km north of the equator).
Answers to Station 9:
a)
6 2
4
b)
2 3
2
c) 2  3
d)
1
2
e) 
1
2
f)
6 2
4
STATION 2
Given ABC where mA = 19, a = 25 and c = 30.
a) Find the missing lengths and sides of ALL POSSIBLE TRIANGLES
b) Find the area of each of the triangles.
Answers to Station 1:

 x  10  c) 3758.77 km south
45
d) 3064.18 km north e) 22.59, 87.41, 112.59, 177.41
a) graph b) y  4000cos
STATION 3
2
3
3
where
    and sec   4 where
   2 , find the exact value of the following,
5
2
2
making sure to express your answers in simple radical form.
Given sin  
a) sin(   )
b) cos(   )
c) cos(2 )
d) sin(2 )
 
e) cos  
2


f) sin    
2

Answers to Station 2:
a) Triangle 1: mA = 23, mB = 138, b = 51.38 Triangle 2: mA = 157, mB = 4, b = 5.36
b) Area of Triangle 1: 292.99 sq. units Area of Triangle 2: 26.16 sq. units
STATION 4
Focus, focus on math I do say
Don’t go off on a tangent when understanding tangent is at play


a) Graph f (x)  tan  x    2 from 2  x  2 .
4

b) Write the equations of the asymptotes in part (a)
1
c) Find the angle that the line y   x  2 makes with the x-axis.
3
d) Write the equation of the line that makes a 30 with the x-axis and has a y-intercept of (0, 3)
Answers to Station 3:
2  3 35
 21  2 15
a)
b)
20
20
c)
17
25
d) 
2 15
16
e) 
10
4
f)
1
4
STATION 5
Find the exact value of each of the following for  0,2 

3
a) arccos  

 2 
 1
b) sin1   
 2
c) arctan( 3)
d) tan1 (1)
e) sec1 (2)
f) csc1 ( 2)
 2
g) cos 1 

 2 
h) sin1 (0)
i) arccos(1)
Answers to Station 4:
a) b) y 
3
7

5
, y
, y , y
4
4
4
4
c) 161.57
 3
d) y  
 x  3
 3 
STATION 6
Solve for the exact values of x for  0,2 
a) sin(x) 
3
2
b) cos(x)  
1
2
c) tan(x)  1
Solve for all values of x for  0,2  . Round your answers to the nearest 0.01.
d) 4sin(x)= -3
Answers to Station 5:
2


a)
b) 
c) 
3
6
3
e) 3cos(x) – 1 = -2
d)

2
e)
3
4
3
4
f)
g)
f) 2tan(x) = - 8

h) 0, , 2
4
i) 0
STATION 7
Solve for 0  x  2 :
a) sin(2x)  5cos2 (x)
b) cos(5x)cos(3x)  sin(5x)cos(3x) 
c) 2sin(x)  cos(x)  1
Answers to Station 6:
 2
2 4
,
a) x  ,
b) x 
3 3
3 3
1
2
c) x 
3 7
,
4 4
d) x = 3.99, 5.43
e) x = 1.91, 4.37
f) x = 1.81, 4.95
STATION 8
a) Given that csc(x) = 
17
and x is in quadrant 3, find the values of the 5 other trig functions.
8
b) Find the equation of the sinusoid that passes through a high point of (5, 11) and a low point of (9, -1)


c) What is the period and horizontal shift of y  3sin x  2   1
3

Answers to Station 7:
 3
a) x  , ,1.19,4.33
2 2
b) x 
 5 7 11
, , ,
6 6 6 6
c) x   ,0.93,2.21
STATION 9
Use the trigonometric formulas and identities to find the exact value of each of the following:
a)
b)
c)
d)
e)
cos(15) given that 15 = 45 – 30
sin(15) given that 15 = 30/2
tan (15)
sin(55)cos(25) – sin(25)cos(55)
2sin(165)cos(165)
7  
 7 
f) sin 
 
 given that
12 3 4
 12 
Answers to Station 8:
8
15
17
8
15
a) sin(x)   ,cos(x)   ,sec(x)   ,tan(x)  ,cot(x) 
17
17
15
15
8
6
c) Period = 6 and horizontal shift is
to the left

b) y  6cos

4
 x  5  5