Download Trigonometry

Pre Assessment
• Before you start today’s lesson you must first take
the pre assessment by following this link:
• When you have completed the pre assessment
you can begin the powerpoint. Have your
notebook out, take notes, and make sure you are
answering any questions that appear in the
powerpoint. I will be checking your notes for a
grade at the end of class.
Trigonometry
 Trigonometry is derived from Greek words
trigonon (three angles) and metron ( measure).
 Trigonometry is the branch of mathematics
which deals with triangles, particularly triangles
in a plane where one angle of the triangle is 90
degrees
 Triangles on a sphere are also studied, in
spherical trigonometry.
 Trigonometry specifically deals with the
relationships between the sides and the angles
of triangles, that is, on the trigonometric
functions, and with calculations based on these
functions.
2
Right Triangle
 A triangle in which one angle is
equal to 90 is called right
triangle.
 The side opposite to the right
angle is known as hypotenuse.
AB is the hypotenuse
 The other two sides are known
as legs. When a specific angle is
being referenced the legs are
called either adjacent or
opposite to the angle being
referenced.
AC and BC are the legs
Trigonometry deals with Right Triangles
3
Hyp, Opp, and Adj
• In Geometry you learned about three
trigonometric ratios: Sine, Cosine, and Tangent.
Before we can go deeper into the study of those
ratios we must know the following terminology.
• The hypotenuse (hyp) is the longest side of the
triangle – it never changes
• The opposite (opp) is the side directly across
from the angle you are considering
• The adjacent (adj) is the side right beside the
angle you are considering
Angle in Question
Use Google to look up the Greek letter theta. Draw theta
in your notes and be sure to label the letter theta. Then
write one or two sentences about how theta is used in
mathematics.
Task 1: Draw the following picture in your
notes. Label angle BAC with the theta symbol.
If angle BAC is theta,
a. Label the hypotenuse
b. Label the opposite leg
c. Label the adjacent leg
Trigonometric Ratios
We can form a total of six ratios using the three any triangle. The first
three ratios are below.
Name
“say”
Abbreviatio
n
Abbrev.
Ratio of an
angle
measure
Sine
Cosine
Tangent
Sin
Cos
Tan
Sinθ = opposite side
hypotenuse
cosθ = adjacent side
hypotenuse
tanθ =opposite side
adjacent side
Task 2: Make sure you have these
ratios in your notes.
opp
sin  
hyp
adj
cos 
hyp
opp
tan  
adj
Tan
Opposite
Adjacent
Sin isis Opposite
Cos
Adjacent over
over Hypotenuse
Hypotenuse
SOHCAHTOA
Task 3: Answer the six questions
below: 1. Write the ratio for sin A
B
c
2. Write the ratio for cos A
a
C
b
A
3. Write the ratio for tan A
#’s 4 – 6: Let’s switch angles: Find the sin, cos and tan for Angle B:
Trigonometric Ratios and Special
Right Triangles
Task 4 to be completed in your notes:
1. Draw triangle ABC as a 30° – 60° – 90° triangle.
2. Label the hypotenuse 1 unit in length.
3. Label the shortest leg as .5 units in length.
4. Use the Pythagorean theorem to determine length of the
longest leg.
5. Now that you know all the side lengths determine the following:
a. sin(30) = _____
b. cos(30) =_____ c. tan(30) = ____.
Trigonometric Ratios and Special
Right Triangles
Task 5 to be completed in your notes:
1. Draw triangle ABC as a 45° – 45° – 90° triangle.
2. Label the hypotenuse 1 unit in length.
3. Determine the length of the legs and label it in your diagram.
4. Now that you know all the side lengths determine the following:
a. sin(45) = _____
b. cos(45) =_____ c. tan(45) = ____.
You have now completed the review of Geometry level
Trigonometry.
In Algebra II we will study sine, cosine, tangents and their
reciprocals as they relate to a unit circle.
Please raise your hand so that I may check your answers, and give
you permission to proceed to the next slides.
Chapter 13 – Trigonometry Notes
Task 6: Copy the following definitions into your notes.
Include pictures for reference.
Task 7: Copy the picture of the clock into your notes and answer
the questions.
y
1. In which quadrant does the terminal side
of 2:35 lie?
2. Is 3:00 an angle in standard position?
x
3. Explain why 9:00 is not an angle in
standard position using the words
terminal side and initial side.
4. What is the positive angle measurement
created by the hands of the clock when
the clock strikes 3:00pm?
5. What is the negative angle measurement
created by the hands of the clock when
the clock strikes 3:00pm?
Measuring Angles
Angles can be measured in two ways:
•Degrees
•Radians
Degrees…
Radians…
Task 8: Determine the angle measure (in degrees) of each angle inside this circle
created by the positive x-axis and the various terminal sides. Type your answers in each
box provided.
90
60
45
30
180
0 or 360
225
300
Task 9:
In order to complete the same circle in radian measure, we must
first learn what a radian is…
1. Research radians on this website: Make sure you hit the play
button if there is one.
http://www.mathsisfun.com/geometry/radians.html
2. In your notes record the definition of a radian, and write a few
sentences summarizing what you learned from the website.
3. Copy these conversion to notes.
Task 10: Convert all the angles in our previous circle to radian measure. Leave all your
answers as fractions with pi in it. NO DECMIALS
π/2
0π
Homework
1.
2.
Read page 830 in your textbook about coterminal angles or research coterminal angles on
the internet.