ACT Prep - Campbell County Schools
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Transcript ACT Prep - Campbell County Schools
ACT PREP
Mathematics β Trigonometry
DON'T FORGET CALCULATOR!
MODE: DEGREES!
Mathematics β Trigonometry
TRIGONOMETRY
Overview
Trigonometry (7%). Questions in this content area are based on
understanding trigonometric relations in right triangles; values and
properties of trigonometric functions; graphing trigonometric functions;
modeling using trigonometric functions; use of trigonometric identities; and
solving trigonometric equations.
β
Topic
Basic
Skills
Application
Analysis
Total
Pre-Algebra/Algebra
8
12
4
24
Intermediate Algebra/
Coordinate Geometry
7
7
4
18
Plane Geometry
6
8
0
14
Trigonometry
2
2
0
4
TRIGONOMETRY
Trigonometric Functions for special angles
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TRIGONOMETRY- THE UNIT CIRCLE
ALL POINTS ON THE CIRCLE ARE REPRESENTED BY (COSπ½, SINπ½)
β Quadrants
β 1 Degree = 1/360 of a
revolution (full circle)
β Radians
o Angle with arc length = r
o 1 degree = Ο/180 radians
o 1 radian = 180o/Ο
98% of the time,
this is given in the
problem!
TRIGONOMETRY- THE UNIT CIRCLE
EXAMPLES
1. What quadrant is the angle
210o?
π
2. How about radians?
4
A TOUGH ONE:
If π = 150π, what is the value of
sinπ?
TRIGONOMETRY
β
β
Coterminal Angles
β Angles that common
terminal and initial sides
Add or subtract multiple of 360o
(2Ο for radians) to find
coterminal angles
TRIGONOMETRY
Six Trigonometric Ratios
π πππ =
πππ π =
π‘πππ =
ππ ππ =
π πππ =
πππ‘π =
πππ π¦
=
βπ¦π π
πππ π₯
=
βπ¦π π
πππ π¦
=
πππ π₯
1
βπ¦π π
=
=
π πππ πππ π¦
1
βπ¦π π
=
=
πππ π πππ π₯
1
πππ π₯
=
=
π‘πππ πππ π¦
TRIGONOMETRY
Graph of Sin(x)
TRIGONOMETRY
Graph of Cos(x)
TRIGONOMETRY
Graph of Tan(x)
TRIGONOMETRY
Trig Identities⦠for any trig value (not just right triangles!)
sin2 π + cos 2 π = 1
sin π
tan π =
cos π
Example:
Find tanx if sinx = ½ and cosx = 1/3
TRIGONOMETRY
Solving Nonright Triangles (pg. 308)
TRIGONOMETRY
Practice Problems
β
Which of the following is the sine of A in the right triangle
below?
A. 5/13
B. 5/12
C. 12/13
D. 12/5
E. 13/5
β
β
β
β
β
β
β
β
β
β
β
Which of the following expressions is the closest approximation
to the height h, in feet, of the roof truss shown below?
A. 15 tan 20°
B. 15 sin 20°
C. 30 tan 20°
D. 30 sin 20°
E. 15/sin 20°
β’In the figure below, points A and B are on opposite banks of a small
stream. Point C is on the same bank of the stream as point B and
approximately 18 meters from B. The measure of β CBA is 45°, and the
measure of β BCA is 60°.
β’Which of the following expressions gives the approximate distance,
in meters, between point A and point B ?(Note: For ΞPQR, where p, q,
and r are the lengths of the sides opposite β P, β Q, and β R,
respectively, sinP/p=sinQ/q=sinR/r.)
-A. sin60/18sin45
-B. sin60/18sin75
-C. 18sin45/sin60
-D. 18sin60/sin45
-E. 18sin60/sin75
TRIGONOMETRY
Practice Problems
β
Which of the following is equivalent to sin(x) csc(βx) wherever
sin(x) csc(βx) is defined?
βF. β1
βG. 1
βH. βtan
βJ. tan
2
βK. βsin