Transcript Trigonometry Review

August 20-21, 2014
Why do we need trigonometry?
Trig allows us to calculate the sides or angles of right
triangles
We will use trig constantly in the first three quarters of
physics … basically anytime something happens at an
angle.
Examples:
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

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Finding resultant velocity of a plane that travels first in one
direction, then another
Calculating the time, path, or velocity of a ball thrown at an angle
Predicting the course of a ball after a collision
Calculating the strength of attraction between charges in space
etc., etc., etc
Right triangles
The formulas that we learn today work only with right
triangles … but that’s ok, we can create a right triangle to
solve any physics problem involving angles!
But, it does beg the question … what’s a right triangle?
a triangle with a 90o angle
Calculating the length of the
sides of a right triangle
 If you know the length of two of the sides, then use …
the Pythagorean Theorem: c2 = a2 + b2
Example:
NOTE:
A = 3 cm, B = 4 cm, what is C?
“C” always refers to the hypotenuse!
C2 = (3cm)2 + (4cm) 2
The hypotenuse is always the
longest
side2and its always the side
2
C = 25cm
that is opposite of the right angle.
C = 5 cm
Work on individually. Find the missing side.
z
9m
1 mm
y
x
2 mm
6 cm
7m
X=6m
2 cm
Y =6
cm
Z = 2 mm
Calculating the length of the
sides of a right triangle
 What if we have one side and one angle? How do we
find the other sides?
We can use the trig functions: sin, cos, and tan
sin θ = Opposite / Hypotenuse
cos θ = Adjacent / Hypotenuse
tan θ = Opposite / Adjacent
Examples:
25
cm
θ = 25 degrees
5m
y
θ = 30 degrees
Find y and x
x
Examples:
25
cm
θ = 25 degrees
5m
y
θ = 30 degrees
x
Find y and x
sin(30) = y/25cm
25cm*sin(30) = y
13 cm = y
tan (25) = 5m / x
x = 5m / tan(25)
x = 11 m
Examples:
z
θ = 35 degrees
y
18 cm
θ = 40 degrees
Find z and y
6m
Examples:
z
θ = 35 degrees
y
18 cm
θ = 40 degrees
6m
Find z and y
sin (40) = 18 cm / z
z = 28 cm
tan (35) = y / 6m
y=4m
Calculating the angles of right triangle
 In any triangle (right or not) the angles add to 180o.
Example: Find a
A = 180 – 70 – 50 = 60o
Calculating the angles of right triangle
 In right triangles, we can also find the angle using the
side lengths and inverse trig functions
sin-1 (opp / hyp) = θ
cos-1 (adj / hyp) = θ
tan-1 (opp / adj) = θ
Examples:
25
cm
18 cm
θ=?
Find θ and φ
φ=?
6m
11 m
Examples:
25
cm
18 cm
θ=?
φ=?
6m
11 m
Find θ and φ
sin-1 (18cm / 25cm) = θ
θ = 46 degrees
tan-1 (6 m / 11m) = φ
φ = 29 degrees
Examples:
θ=?
φ=?
12 m
8cm
9cm
Find θ and φ
10 m
Examples:
θ=?
φ=?
12 m
8cm
9cm
10 m
Find θ and φ
tan-1 (8cm / 9cm) = θ
θ = 42 degrees
cos-1 (10 m / 12m) = φ
φ = 34 degrees
Mixed Practice
Find all sides and angles
Closure, HW, & Exit Ticket
Closure –
 What were our objectives today, and how well did we
accomplish them?
 How did we address our unit statement today?
 What was our LP trait and how did we demonstrate it?
HW –
 LAB!
 Trig HW (HW QUIZ NEXT CLASS)
Exit Ticket Handout -