Section 2.1
If A and B are complementary angles then cos A = sin B. Sine and cosine are
cofunctions.
Cofunction Identities
sin A = cos(90° - A)
sec A = csc(90° - A)
tan A = cot(90° - A)
45° - 45° - 90° Triangles
30° - 60° - 90° Triangles
cos A = sin(90° - A)
csc A = sec(90° - A)
cot A = tan(90° - A)
1. Find the sine, cosine, and tangent values for angle A and B.
2. Given a right triangle ABC, and the given values find all 6
trigonometric values.
a) a = 3, c = 10
2. Given a right triangle ABC, and the given values find all 6
trigonometric values.
b) a = 8, b = 11
3. Writing Functions in terms of its co-functions.
a) cos 52
b) tan 71
c) sec 24
4. Solving Equations using co-function identities.
a) cos( + 4) = sin(3 + 2)
b) tan(2 - 18) = cot( + 18)
c) sec(3 + 10) = csc( + 8)
4. Determine whether the statement is true or false.
a) sin 21 > sin 18
b) sec 56 < sec 49
Find the exact value of each.
1. tan 30°
2. sin 30°
3. sec 30°
4. csc 45°
5. cos 45°
6. sin 60 °
7. tan 60°
Section 2.2
A _____________________ angle is a positive acute angle measured from the
terminal side of an angle to the ___________________
Reference Angles
An angle ’ is a positive acute angle made by the terminal side of the
angle  and the x-axis.
A reference angle can be expressed as a 30°, 45°, or a 60° angle and then we
can use the information that we know from those triangles to find the values of
the six trig functions of the reference angle.
1. Find the reference angles for the given angle.
a) 278
b) -125
c) 99
d) -1387
2. Find the 6 trig functions for each angle. Use reference angles.
a) 210
b) - 315
c) 120
3. Evaluating Expressions with Functional Values of Special Angles
a) cos 120 + sin2 60 - tan2 30
b) cos2 60 + sec2 150 - csc2 210
4. Find all values of , if  is an angle [0,360] for each.
a) cos  =
-
2
2
b) tan =undefined
c) csc  = 2
Section 2.3
Calculators can be used to find the values of the six trig functions for angles.
The angles must be written as a ________________ to be entered into the
calculator. Make sure your calculator is in _______________ mode
Sin, Cos, and Tan are used to convert _____________ to ratios.
are used to convert ______________ to angles
1.Calculate the value of each expression.
a) sin 49 12’
b) sec 97.977
c) cos(-246)
d) 1/cot(51.4283)
e) tan77
f) csc(-140)
2. Finding Angle Measures using a calculator.
a) sin  = .9677
b) sec  = 1.054
c) tan  = 5.876
Section 2.4
Trig functions are used to solve ___________ triangles.
Angles of ____________________ are measured from a horizontal line up to the line
of sight to the object.
Angles of _______________________ are measured from a horizontal down to the line
of sight to the object.
1.
2.
3.
4.
How tall is a flagpole that casts a 12-foot shadow when the sun is at an angle of 75° above
the horizon?
A kite on the end of a 250-foot string is at an angle of 35° above horizontal. How high is the
kite above the ground? Assume the string is a straight line.
For safety and noise abatement, landing aircraft are required to be 1500 feet above the
ground when they are 25000 feet from the end of the runway (horizontal distance). What is
the angle of the glide slope that makes this possible?
An airplanes distance measuring equipment measures the slant range distance from the
aircraft to the navigational aid. If an aircraft is 17.56 miles slant range distance from a
navigational aid and is flying two miles above the ground, what is the distance along the
ground from the airplane to the navigational aid? Do not use the Pythagorean Theorem.
Section 2.5
The term _______________ is used in navigation to designate a direction. If the
bearing is expressed only in degrees, it is measured from a _________________line.
Bearings may also be measured from either a _______________ or _____________ line
and would be expressed in terms such as N35°W or S50°E.
1.
2.
3.
A surveyor on a mountain road 524 feet above a lake was asked to
calculate the distance across the lake. The surveyor measured the
angle of depression to the near and far edges of the lake to be 66°
and 27° respectively. Determine the distance across the lake.
To determine the height of a mountain, a surveyor measured the
angle of elevation to the top of the mountain from two points 500 feet
apart. The two angles of elevation were 35° and 40°. To the nearest
10 feet, how high is the mountain?
Veronica and Jose are located one mile apart on the ground. They
observe a blimp directly above the road connecting them. Jose
measures the angle of elevation to the blimp to be 53°; Veronica
measures the angle of elevation to the blimp as 22°. Find the height of
the blimp above the ground.
The Empire State Building is observed directly south of tourist A. A
second tourist is 15 miles due west from tourist A finds the bearing to
the Empire State Building to be S35.7°E. How far is the Empire State
Building from tourist B?