Download Sect 1.1 Angle: Standard Position: Quadrantal Angles: Acute Angle

MAT 182 Chapter 1
Fitzgerald
Sect 1.1
Angle:
Standard Position:
Quadrantal Angles:
Acute Angle:
Right Angle:
Obtuse Angle:
Straight Angle:
Complementary Angles:
Supplementary Angles:
Find the complement and supplement angles of 40o.
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MAT 182 Chapter 1
Fitzgerald
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Solve for x and y.
6x 1
2x 1
7 y 11
9y  25
Breaking down a degree.
Minute:
Second:
Perform each calculation.
5129'3246'
90  1837'
Converting Degrees, Minutes, and Seconds to a decimal degree and vise versa.
Convert 21 8' 14"
Convert 34.2678 to degrees,
to a decimal degree.
Minutes, and seconds to nearest sec.
MAT 182 Chapter 1
Fitzgerald
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Coterminal Angles:
Assume the following angles are in standard position. Find a positive angle less
than 360o that is coterminal with each of the following:
a. a 400o angle.
b. a – 855o angle.
CD players always spin at the same speed. Suppose a player makes 480 revolutions
per min. Through how many degrees will a point on the edge of the CD move in 2
seconds?
Sect. 1.2
Angle Relationships
1
2
3
4
5
Vertical Angles:
Corresponding Angles:
Alternate Interior Angles:
Alternate Exterior Angles:
Same Side Interior Angles:
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6
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MAT 182 Chapter 1
Fitzgerald
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Sum of the angles of a triangle_____________________________________.
Types of Triangles:
Angles
Acute Triangle:
Right Triangle:
Obtuse Triangle:
Sides
Equilateral Triangle:
Isosceles Triangle:
Scalene Triangle:
Similar Triangles:
Conditions:
Labeling:
ABC ~ RST
MAT 182 Chapter 1
Fitzgerald
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Sect. 1.3 Trigonometric Functions.
Definitions of Trigonometric Functions of Any Angle
Let  be any angle in standard position and let P = (x, y) be a point on the terminal
2
2
side of  . If r  x  y is the distance from (0, 0) to (x, y), the six
trigonometric functions of  are defined by the following ratios:
Let P = (8, 15) be a point on the terminal side of  . Find each of the six
trigonometric functions of  . P = (8, 15) is a point on the terminal side of  .
x = 8 and y = 15.
MAT 182 Chapter 1
Fitzgerald
Let P = (1, –3) be a point on the terminal side of  . Find each of the six
trigonometric functions of  . P = (1, –3) is a point on the terminal side of  .
x = 1 and y = –3.
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MAT 182 Chapter 1
Fitzgerald
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Section 1.4
Reciprocal Identities.
sin   
csc  
cos  
sec  
tan  
cot   
Find the sign value of the trigonometric functions for each quadrant and the range
values of the six trigonometric functions.
y  sin 
y  csc 
y  cos 
y  sec 
y  tan 
y  cot  
Suppose sin   
functions.
y  sin 
y  cos 
y
x
y  tan 
y  cot  
y  sec 
y  csc 
2
and tan   0 . Find the values of the other five trigonometric
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MAT 182 Chapter 1
Pythagorean Identities.
x2  y 2  r 2
Quotient Identities.
sin  

cos 
Fitzgerald
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r  x2  y 2  x2  y 2  r 2
x2  y 2  r 2
x2  y 2  r 2
cos 

sin  
Find sin   and tan  , given that cos   
3
4
and sin   0 .
Find sin   and cos  , given that tan   43 and  is quadrant 3.