Transcript An angle of 1 radian is shown for each circle below

Station 1 – What is a radian
An angle of 1 radian is shown for each circle
below. Define what is meant by a radian. Also,
what would be meant by an angle of 3 radians?
Station 2 – Converting between angular units
1) Convert 3°10’ 20” to degrees
2) Convert 40.125° into degree, minute, seconds
both 1 & 2 you want to be able to do it both
(a.k.a “DMS”) For
with and without a calculator. Make sure you
ask if you forget how to do it on the calculator.
3)
4)
5)
6)
7)
Convert 620° to radians
7

Convert 8 to degrees
Find the supplement of 60°30’ in radians.
How do you convert from degrees to radians?
How do you convert from radians to degrees?
Station 3 – Arc Length
s = rθ
1) In the above formula for arc length, what
do s, r and θ each represent? Is there
anything special about θ?
2) What arc length is cut by a 110° central
angle within a circle of diameter 12in?
Station 4 – RPMs
Example 5: pg.323
Albert Juarez’s truck has wheels 36in in
diameter. If the wheels are rotating at 630
rpm (revolutions per minute), find the
truck’s speed in miles per hour.
Hint: Think unit conversions and remember
a revolution is equivalent to turning one full
circular angle. Also, use what you
learned/recalled from Station 1.
Station 5 – Finding trig ratios from a triangle
1) What is SOHCAHTOA?
2) Find all the below trigonometric ratios for the
indicated triangle.
B
a) sin(A)
b) tan(B)
4
c) cot(A)
d) cos(B)
A
C
5
e) sec(A)
These last two are ones where you’re going to have to
f) csc(90°-A)
think a little harder. Think critically about what each one
really asking for. Don’t get locked into trying the same
g) cos(C) isprocess
you’ve been doing necessarily. At the BC level,
you should never just be memorizing a process. That
will lead you down a dangerous road with grades lower
than you’re used to getting.
Station 6 – Finding trig ratios from given ratios
Trigonometric Identities
p. 404 & 405 in text
These are identitites you MUST (still and forever) know by heart
Reciprocal Identities
1
sin  
csc 
1
csc  
sin 
1
cos  
sec 
1
sec  
cos 
Quotient Identities
sin 
tan  
cos 
1
tan  
cot 
cot  
1
tan 
cos 
cot  
sin 
Pythagorean Identities
sin 2   cos 2   1
1  tan 2   sec2 
1  cot 2   csc2 
Station 6 – Finding trig ratios from given ratios
1) Given sinθ = ¼ find all five other
trig functions for θ given θ is acute.
Station 6 continued
3
2
2) Given csc t = 3 and sec t =
4
Find…
a) cos t
NOTE: You do not have to rationalize
denominators unless you want to in
Analysis BC
b) cot t
c) cos (π/2 – t)
*a thinker problem…hmm what is special about that angle…
Station 7 – Evaluating using the unit circle (NO CALCULATOR)
Evaluate
 31 
1) sin 

 6 
5) sec  420
o
2) tan  24 

 5 
6) csc 

6


 13 
3) cos 

 4 
 
4) sin  
2
 2 
7) cot 

 3 
 4 
8) cos  

 3 
Find t in radians (0 < t < π/2).
Don’t use a calc! That’s cheating!!!
2 3
a) csc t =
3
b) sin t =
2
2
Station 8 – Evaluating using the calculator (Make sure you check your MODE)
Evaluate
1) sin  31
o

2) tan  2
 
3) cos  
8
4) sec  400o 
Find t in radians (0 < t < π/2).
a) csc t = 5
b) sin t = 0.2
c) cos t = 2
Station 9 – Finding missing parts of right triangles (careful of your MODE again)
1) Given A = 21° and a = 15, solve
the right triangle.
B
“Solve the triangle” means find
all missing sides and angles.
C
A
Remember: Lower case letters
are used to denote sides, and
upper case letters are used to
denote angles. Also, a is the side
across from angle A, b is the side
across from angle B, etc.
Station 9 cont.
2) Solve for x. Don’t round ever!!!
Use the “Ans” or the >Sto (store) feature of your calculator.
Ask if you don’t know how.
x
10
45°
70°
15
Station 10 – Word Problem
Sadly you are leaving Banff, Canada and the lovely Canadian
Rockies behind. You stop at two different scenic viewpoints. At the
first viewpoint you have to tilt your binoculars to an angle of
elevation of 9° to look back longingly at the snow capped peak.
After narrowly avoiding a moose you complete the 13mi drive to the
second view point where you only have to tilt your binoculars 3.5° to
see the same peak. Exactly how tall is the mountain? Make sure
you can get the answer exactly with NO rounding error. Also be
sure to show ALL steps as if it were a quiz/test problem.
Very majestic
mountain…
3.5°
13mi
9°