Download Solving a right triangle

7.3
Evaluating Trig Functions of
Acute Angles
In this section, we will study the following topics:
Evaluating
trig functions of acute angles using right
triangles
Using
trigonometry to solve right triangles
1
I AM A VERY IMPORTANT SLIDE!
Special Right Triangles
The 45º- 45º- 90º Triangle
Ratio of the sides:
Find the exact values of the six trig functions for 45
45º
2
1
45º
sin 45° =
csc 45° =
cos 45° =
sec 45° =
tan 45° =
cot 45° =
1
MEMORIZE!
2
I AM A VERY IMPORTANT SLIDE, TOO!
Special Right Triangles
The 30º- 60º- 90º Triangle
Ratio of the sides:
30º
Find the exact values of the six trig functions for 30
sin 30 =
csc 30 =
cos 30 =
sec 30 =
tan 30 =
cot 30 =
2
3
60º
1
MEMORIZE!
3
DON’T FORGET ABOUT ME!
Special Right Triangles
The 30º- 60º- 90º Triangle
Ratio of the sides:
Find the exact values of the six trig functions for 60
30º
2
3
60º
sin 60 =
csc 60 =
cos 60 =
sec 60 =
tan 60 =
cot 60 =
1
MEMORIZE!
4
Find the exact value of each expression.
(a) sin
2

3
 tan
2

4
(b) sin 60 cos 45
(c) cos

3
 cot

4
Using the calculator to evaluate trig
functions
To evaluate trig functions of acute angles other than 30, 45, and 60,
you will use the calculator.
Your calculator has keys marked   .
**Make sure the MODE is set to the correct unit of angle measure.
(Degree vs. Radian)
Example:
Find
tan 1.25 to two decimal places.
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Using the calculator to evaluate trig
functions
To find the values of the remaining three functions (cosecant,
secant, and tangent), use the reciprocal identities.
WARNING: DO NOT USE THE INVERSE FUNCTIONS; e.g. SIN-1
Example:
(Give answers to three decimal places)
1. Find
csc73.2
2. Find cot 11 38' 56"
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Solving a right triangle
When you are given two sides of a right triangle and you want to find
the angle OR when you are given one side and one acute angle and
you want to find one of the remaining sides, you will use a process
called solving right triangles.
PLAN
Sketch
Use
If
a right triangle and label the angle and/or side(s) given
the definitions of the six trig functions to determine which
function is appropriate to use.
you have angles of 30º, 60º, or 45º, use the special reference
triangles (ratios of the sides) to solve the triangle.
Otherwise, use your calculator to evaluate the trig function.
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Solving a right triangle
Example
Solve the triangle.
Solution:
52º
9.6
Reminder: Make sure your MODE is
set to “Degree”
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
End of Section 7.3
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