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 (a.k.a “DMS”)
For both 1 & 2 you want to be able to do it both with and without a calculator. Make sure you ask if you forget how to do it on the calculator.
3) Convert 620 ° to radians 4) Convert 7 to degrees 8 5) Find the supplement of 60 °30’ in radians.
6) How do you convert from degrees to radians?
7) How do you convert from radians to degrees?
Station 3 – Arc Length
s = r θ
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) c) cot(A) d) cos(B) A 5 C e) sec(A) f) csc(90 g) cos(C) °-A) is really asking for. Don’t get locked into trying the same process 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. 4
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
sin csc 1 csc 1 sin cos sec 1 sec 1 cos tan cot 1 cot 1 tan
Quotient Identities
tan sin cos cot cos sin
Pythagorean Identities
sin 2 cos 2 1 2 sec 2 2 csc 2
Station 6 – Finding trig ratios from given ratios
1) Given sin θ = ¼ find all five other trig functions for θ given θ is acute.
Station 6 continued
2) Given csc
t
Find… a) cos
t
= 3 and sec
t
=
3 2 4
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 2) tan 24 3) cos 13 4
o
6) csc 5 6 7) cot 2 3 Find
t
in radians (0 <
t
< π/2). Don’t use a calc! That’s cheating!!!
a) csc
t
= 2 3 3 b) sin
t
= 2 2 4) sin 8) cos 4 3
Station 8 – Evaluating using the calculator (Make sure you check your MODE)
Evaluate 2) tan 3) cos Find
t
in radians (0 <
t
< π/2). a) csc
t
= 5 b) sin
t
= 0.2
c) cos
t
= 2
o
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.
10 45 ° x 15 70 °
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 sure to show
ALL exactly
with
NO
rounding error. Also be steps as if it were a quiz/test problem.
Very majestic mountain…
3.5
° 13mi 9 °