Download Lecture 2 (L2): Right Triangle Trigonometry Textbook Section: 4.3

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Lecture 2 (L2): Right Triangle Trigonometry
Textbook Section: 4.3
Geometry Review:
Triangle:
Scalene Triangle:
Isosceles Triangle:
Equilateral Triangle:
Right Triangle:
Parts of Right Triangles:
A right triangle has two ________________________________ and one________________________.
The side opposite the right angle is called the_________________________________ and it is the
______________________________ of the sides. If we consider one acute angle, 𝜃, the side across
from that angle is called the _________________________________ and the side that helps form the
angle, but is not the _____________________________, is called the ____________________________________.
Diagram:
Pythagorean Theorem:
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Six Trigonometric Functions for Right Triangles:
Consider an acute angle, 𝜃, of a right triangle. The
_____________________________________________________________________ of that angle are defined by
_____________________________________ of particular side lengths of the triangle.
The functions are__________________________, _______________________________,
_______________________________, _______________________________ , _______________________________, and
_______________________________.
Diagram and Definitions:
Mnemonic Device:
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Problem: Find the six trigonometric functions of an acute angle, 𝜃, for a right triangle with
hypotenuse of length 13cm and the side opposite 𝜃 a length of 5cm.
Problem: Given cos 𝜃 =
3
4
find the other five trigonometric functions.
Problem: Find the six trigonometric functions of a right triangle with one acute angle that
measures
𝜋
4
radians or 45° and adjacent side length of 1in.
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Problem: Given a right triangle with acute angle
𝜋
6
, an opposite side length of 1cm, and a
hypotenuse of length 2cm, find the function values of sin
Problem: Given a right triangle with acute angle
𝜋
6
𝜋
6
, cos
𝜋
6
𝜋
, 𝑎𝑛𝑑 tan .
6
, an opposite side length of 1cm, and a
hypotenuse of length 2cm, find the function values for sin
𝜋
3
, cos
𝜋
3
𝜋
, 𝑎𝑛𝑑 tan .
3
Special Angles:
The special angles in trigonometry are ___________________________________________________.
Cofunctions:
A _____________________________ of a trig function, 𝑓, is a function, 𝑔, such that
if_________________________________, then _______________________________________________________________.
Examples:
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Cofunction Identities:
If 𝜃 is an __________________________________then the following relationships hold:
Problem: Evaluate cos 66° − sin 24° .
Problem: Evaluate
tan 58°
cot 32°
.
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Trigonometric Identities:
Due to their nature, there exists many relationships between the trigonometric
functions.
Problem: Given a right triangle with acute angle, 𝜃, evaluate
1
sin 𝜃
.
Reciprocal Identities:
Problem: Given a right triangle with acute angle, 𝜃, evaluate
Quotient Identities:
6
sin 𝜃
cos 𝜃
.
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Pythagorean Identities:
Notation:
Problem: Given an acute angle, 𝜃, with cot 𝜃 = √2 , find the value of tan 𝜃 and csc 𝜃 .
Applications:
The _______________________________________________ is the angle from the horizontal
_________________________. The _______________________________________________ is the angle from the
horizontal _________________________________.
Diagram:
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MAC1114 Lecture Note Outlines_Eichler
Problem: You are standing 30 meters away from an apartment complex. You estimate that
𝜋
the angle of elevation to the 5th floor measures radians. The total height of the complex
3
measures an addition 10 meters above the 5th floor. What is the height of the complex?
What is the distance between you and a window on the 5th floor?
Problem: You are walking towards a flagpole. The angle of elevation from the ground to
the top of the flagpole is 30° . After walking 12 feet, the angle of elevation is now 45° . What
is the height of the flagpole?
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