Download Trigonometry

Trigonometry
Final Exam Review Material
The Logistics
Two Parts
Free Response – 4 Questions consisting of
Word Problem(s)
– Setting up a triangle and solving
Graphing
Verifying
Multiple Choice
54 Questions
– 74 TOTAL POSSIBLE POINTS!
Key Terms
Standard Position
An angle whose vertex is at the origin and initial side is
on the positive x – axis.
Initial Side
Ray of an angle that represents the starting off point of
rotation.
Terminal Side
Ray of an angle that represents the ending point of a
rotation.
Key Terms
Co-Terminal Angle
Angles that have the same initial side and the
same terminal side
Example – 45 degrees and 405 degrees
Quadrantal Angles
Angles whose terminal side lie on an axis.
Example 0, 90, 180 and 270…
Values are ALWAYS either -1, 0, 1 or undefined.
Key Terms
Co-functions
Trigonometric functions that have the same
value.
Occurs with complementary angles
Example – sin30 = cos60
30+60 = 90 a complementary angle
Reference Angle
The positive acute angle made by the terminal
side of any angle and the x - axis
Key Terms
Arc Length
The measure of the portion of a circle
intercepted by some central angle
Arc Length = (Angle Measure in Radian Mode)(radius)
Sector of a Circle
The AREA of a portion of a circle intercepted
by some central angle
Sector = ½ (radius squared)(Angle Measure in Radian Mode)
Key Terms
Graphing
Know amplitude, period, phase shift, vertical
shift
Be able to identify asymptotes of the tangent
and cotangent functions
Example 1
Find the six trigonometric functions for an
angle in standard position that has the point
(-3, -7) on its terminal side.
Example 2
Find the smallest positive angle co-terminal
with 13,267 degrees.
Example 3
Find the arc length and area of a sector of a
circle intercepted by a central angle of 42
degrees with a radius of 10 mm.
Example 4

Graph the function y  1  2 csc 4( x  )
4
Over a two period interval
Example 5
Verify 1  cos x  1  cos x  4cot x csc x
1  cos x 1  cos x
Example 6
Find the sin(x+y), cos(x–y) and tan(x+y)
given sinx = -1/4, cosy = -4/5, x and y in
QIII.
Example 7
Solve the following equation on the interval
[0, 360) cos2x + cos x = 0
Example 8
1
Evaluate cos(2sin (  ))
3
1
Example 9
Find the real number
solution to
1
y  tan ( 3)
Example 10
Solve triangle ABC given C = 28.3 degrees,
b = 5.71 inches and a = 4.21 inches.