Download Questions Over Section 1.5 Section 2.1 Right Triangle Trigonometry

Questions Over Section 1.5
Section 2.1­ Right Triangle Trigonometry
There are no conflicts between the right triangle definitions and the coordinate definitions. We will use both techniques throughout the term.
Recall that complementary angles add to _________
Angle: Complementary Angle:
A + B + C = ______
A
A + B = ______
C
A = B
B = Cofunctions of complementary angles are equal.
Examples:
sin 30o = cos _______
tan 10o = cot _______
cos 7o = sin _______
csc 72o = sec _______
Simplify without a calculator:
sin2 20o + sin2 70o
Let's find the exact values of the six trigonometric functions for 30o and 60o .
sin 30o =
csc 30o =
cos 30o =
sec 30o =
tan 30o =
cot 30o =
sin 60o =
csc 60o =
cos 60o =
sec 60o =
tan 60o =
cot 60o =
Section 2.2 Degrees and Minutes
Example: Convert 24o 12' to decimal degrees.
Example: Convert 18.6o to degrees and minutes.
Working with degrees and minutes: Be able to add and subrtact
Example: Find 24o 12' + 17o 56'
Example: Find 180o - 16o 4'
Calculating trig values with degrees and minutes:
Example: Find tan(15o 11')
Example: Find csc 30'
Using Inverse Trigonometric Functions
Inverse trig functions allow us to solve for the original angle.
RECALL FROM ALGEBRA:
solve: 3x = 12 solve x2 = 25
solve sinθ = 0.4
We will work hard with the inverse trig functions.
Example: Solve cosθ = 0.9
Example: Solve cosθ = -0.2
Inverse cosine can give us a Quadrant I or a Quadrant II angle only. Later we will figure out how to get angles in other quadrants that are also solutions.
Example: Find the acute angle θ so that secθ = 2.5.
Section 2.3 Solving Right Triangles
You may ignore the material on significant digits. NOTE: Because we will not be paying attention to significant digits, sometimes our answer will round differently than the back of the book. THAT IS OKAY!
Example: Solve the right triangle given that A = 42o and c = 89 cm.
Example: Solve the right triangle given that c = 45.54 feet and a = 23.32 feet.
Example: Use the figure to find the measure of angle A.
45o
A
B
Example: Use the following figure to find the value of x. Assume C is the center of the circle.
C
26o
19
D
x
A