ACT PREP
Mathematics – Trigonometry
DON'T FORGET CALCULATOR!
MODE: DEGREES!
Mathematics – 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.
●
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
undefined
TRIGONOMETRY- THE UNIT CIRCLE
ALL POINTS ON THE CIRCLE ARE REPRESENTED BY (COS𝜽, SIN𝜽)
● Quadrants
● 1 Degree = 1/360 of a
revolution (full circle)
● Radians
o Angle with arc length = r
o 1 degree = π/180 radians
o 1 radian = 180o/π
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 𝜃 = 150𝑜, what is the value of
sin𝜃?
TRIGONOMETRY
●
●
Coterminal Angles
● Angles that common
terminal and initial sides
Add or subtract multiple of 360o
(2π for radians) to find
coterminal angles
TRIGONOMETRY
Six Trigonometric Ratios
𝑠𝑖𝑛𝜃 =
𝑐𝑜𝑠𝜃 =
𝑡𝑎𝑛𝜃 =
𝑐𝑠𝑐𝜃 =
𝑠𝑒𝑐𝜃 =
𝑐𝑜𝑡𝜃 =
𝑜𝑝𝑝 𝑦
=
ℎ𝑦𝑝 𝑟
𝑎𝑑𝑗 𝑥
=
ℎ𝑦𝑝 𝑟
𝑜𝑝𝑝 𝑦
=
𝑎𝑑𝑗 𝑥
1
ℎ𝑦𝑝 𝑟
=
=
𝑠𝑖𝑛𝜃 𝑜𝑝𝑝 𝑦
1
ℎ𝑦𝑝 𝑟
=
=
𝑐𝑜𝑠𝜃 𝑎𝑑𝑗 𝑥
1
𝑎𝑑𝑗 𝑥
=
=
𝑡𝑎𝑛𝜃 𝑜𝑝𝑝 𝑦
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 𝜃 + cos 2 𝜃 = 1
sin 𝜃
tan 𝜃 =
cos 𝜃
Example:
Find tanx if sinx = ½ and cosx = 1/3
TRIGONOMETRY
Solving Nonright Triangles (pg. 308)
TRIGONOMETRY
Practice Problems
●
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
●
●
●
●
●
●
●
●
●
●
●
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°
•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 ∠CBA is 45°, and the
measure of ∠BCA is 60°.
•Which of the following expressions gives the approximate distance,
in meters, between point A and point B ?(Note: For ΔPQR, where p, q,
and r are the lengths of the sides opposite ∠P, ∠Q, and ∠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
●
Which of the following is equivalent to sin(x) csc(–x) wherever
sin(x) csc(–x) is defined?
●F. –1
●G. 1
●H. –tan
●J. tan
2
●K. –sin