Transcript Geometry Unit 8 Trig 7-4

Basic Trig
4/12/2016
Basic
Trigonometry
Basic Trig
4/12/2016
Definitions
Trigonometry – The area of math that
compares the lengths of the sides of a
triangle to the measures of its angles
(The study of triangle measure)
Trigonometric Ratio – A ratio of the lengths
of the sides of a triangle.
Sine, Cosine, and Tangent – The three
most common trigonometric ratios
Basic Trig
4/12/2016
Trigonometric Ratios
sine of  A 
measure of leg opposite  A
measure of hypotenuse
sin A  BC
AB
sine of  B 
measure of leg opposite  B
measure of hypotenuse
sin B  AC
AB
Basic Trig
4/12/2016
Trigonometric Ratios
cosine of  A 
measure of leg adjacent to  A
measure of hypotenuse
cos A  AC
AB
cosine of  B 
measure of leg adjacent to  B
measure of hypotenuse
cos B  BC
AB
Basic Trig
4/12/2016
Trigonometric Ratios
tangent of  A 
measure of leg opposite  A
measure of leg adjacent to  A
tan A  BC
AC
tangent of  B 
measure of leg opposite  B
measure of leg adjacent to B
tan B  AC
BC
Basic Trig
4/12/2016
SOH – CAH - TOA
S ine equals
O pposite over
H ypotenuse
C osine equals
A djacent over
H ypotenuse
T angent equals
O pposite over
A djacent
Basic Trig
4/12/2016
Properties of Trig Ratios
• Sine and Cosine of any angle will always
be less than 1
• Sine of A always equals Cosine of B
• Sine of B always equals Cosine of A
• Tangent A is the reciprocal of Tangent B
• Tangent B is the reciprocal of Tangent A
Basic Trig
4/12/2016
Classwork
7-4 Study Guide and Intervention (Side 1)
SIMPLIFY!!!!!
1) 15/17 2) 8/15
3)
8/17
1) 17.01
2) 48.59
3) 22.62
4) 75.96
5) 24.89
6) 34.22
4) 15/17
5)
4/5
6) 3/4
7)
4/5
8) 3/5
Basic Trig
4/12/2016
Solving For Missing Value
To solve for missing side length:
• Determine which trig ratio will relate to
given angle, given side, and desired side
• Set up equation
• Solve equation, use table to determine trig
value.
Basic Trig
4/12/2016
Inverse Trig Functions
To Find The measure of an Angle:
• Determine which trig ratio will relate the two
given sides and the desired angle
• Write an equation
• Use the table to find the degree measure that
corresponds to ratio value
Basic Trig
4/12/2016
Classwork
7-4 Study Guide and Intervention (Side 2)
1) 15/17 2) 8/15
3)
8/17
1) 17.01
2) 48.59
3) 22.62
4) 75.96
5) 24.89
6) 34.22
4) 15/17
5)
4/5
6) 3/4
7)
4/5
8) 3/5