FUNDAMENTALS OF ALGEBRA 2A CHAPTER
10 POWERPOINT PRESENTATION
TRIGONOMETRY
TRIGONOMETRY
LEARNING TARGETS
• AFTER YOU COMPLETE THIS CHAPTER, YOU WILL
BE ABLE TO:
• DEFINE TRIGONOMETRIC RATIOS
• CHANGE MEDIAN MEASURE TO DEGREE
MEASURE
• DEFINE AND NAME TRIGONOMETRIC RATIOS IN
SPECIAL TRIANGLES
• IDENTIFY GRAPHS OF SINE, COSINE, & TANGENT
• USE THE LAW OF SINES AND COSINES
TRIGONOMETRY RATIOS
• Trigonometry: Comes from the Greek word,
“trigonon” or triangle and “metron” to
measure. The main part of trigonometry is
the right triangle. There are several special
names that define the ratios.
• Cosine, Sine, and Tangent.
• They also have reciprocals (or the opposite)
Here is a chart of the ratios…..
Here is a list of reciprocal ratios…
Chapter Vocabulary
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Degree: 1/360 of a full circle – symbol = ⁰
Minute: 1/60 of a degree, so 1⁰ = 60’
Second: 1/60 of a minute, so 1’ = 60”
Quadrant – four parts of a circle, using Roman
Numerals and numbers counter-clockwise.
Quadrant I = 0⁰ to 90⁰
Quadrant II = 90⁰ to 180⁰
Quadrant III = 180⁰ to 270⁰
Quadrant IV = 270⁰ to 360⁰
What does this look like?
• Radians – the angle between two radii of a
circle, which is cut off on the circumference
by an arc equal in length to the radius.
A 360⁰ Circle
Special Triangles
• 30 – 60 – 90 Triangle
• 45 – 45 – 90 Triangle
• There is a unique relationship to the sides in
these triangles:
Basic Identities
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Reciprocal – opposites
Pythagorean – using Pythagorean Theorem
Quotient – using division
Cofunction – one ratio working with another
Reciprocal Identities
Pythagorean Identities
Quotient Identities
Cofunction Identities
Other Identities
The Unit Circle
• In the unit circle – the radius is 1. The right
triangle for each quadrant is determined by
the reference angle, the angle with the initial
side at 0⁰.
Inverse Trigonometric Functions
• A quick look at the graph for cosine, sine, and
tangent shows that there is one x and y
value. They can pass the vertical line test.
The inverse or opposite function cannot.
• Principal value: The value of a function in a
restricted range.
• Arcsin, Arccos, Arctan are the inverse
functions.
COSINE CURVE
SINE CURVE
TANGENT CURVE
COFUNTCIONS AND
COMPLEMENTARY ANGLES
• COFUNCTIONS OF COMPLETMENTARY
ANGLES ARE EQUAL.
• COFUNTCION PAIRS:
SOLVING THE TRIANGLE
• Solving the triangle: the process to find the
missing sides and angles.
• Law of Sines:
Law of Cosines – Arbitrary Triangles