INTRODUCTION TO INTRODUCTION TO ENGINEERING ENGINEERING TECHNOLOGYTECHNOLOGYSEVENTH EDITIONSEVENTH EDITIONROBERT J. POND & JEFFERY L. ROBERT J. POND & JEFFERY L. RANKINENRANKINEN
CHAPTER 6
RIGHT-TRIANGLE TRIGONOMETRY AND GEOMETRY FOR TECHNOLOGISTS
RIGHT-TRIANGLE RIGHT-TRIANGLE RELATIONSHIPSRELATIONSHIPS• THE 3-4-5 TRIANGLE HAS LEGS MEASURING 3 AND 4
UNITS AND THE HYPOTENUSE MEASURING 5 UNITS
• IT IS A RIGHT TRIANGLE
• SOMETIMES CALLED THE “MAGIC 3-4-5 TRIANGLE”
B
A
a
b
c
Sides are named with lower case letters; such as a, b, c Think of a as altitude and b as base. c is the hypotenuse. Angles are identified by capital letters and are opposite the sides with the same letter.
RIGHT-TRIANGLE RELATIONSHIPSRIGHT-TRIANGLE RELATIONSHIPS• Carpenters still use 3-4-5 Triangle
•When the sides of a right triangle are all integers, it is called a Pythagorean Triple
• PYTHAGOREAN THEOREM
222 bac ► Three angles always total
180º► For a right triangle, angles
A and B total 90º► 2 angles that add to 90º
are called complementary
TRIGONOMETRIC FUNCTIONSTRIGONOMETRIC FUNCTIONS
sideadjacent
side oppositetan
hyponenuse
sideadjacent cos
hyponenuse
side oppositesin
a _ c
=
= b_ c
= a _ b
c
a
b
90o
Inverse Trig functions are used to find angle measurements when you know the sin, cos, or tan. They are written as, for example, inv sin or sin-1 They are not the same as reciprocal functions known as the secant, cosecant, and cotangent.
“sohcahtoa”
A
B
OTHER TRIGONOMETRIC FUNCTIONS
• INVERSE FUNCTIONS, SUCH AS TAN-1, SIN-1 , AND COS -1 , WILL GIVE THE ANGLE VALUE, WHEN THE FUNCTION VALUE IS KNOW. THESE ARE ALSO CALLED ARC TANGENT, ARC SINE, AND ARC COSINE.
• THE COS-1 (0.500) = 30o
• THE COSECANT, SECANT, AND COTANGENT FUNCTIONS ARE RECIPROCALS OF THE SINE, COSINE AND TANGENT FUNCTIONS• HYPOTENUSE OPPOSITE SIDE
HYPOTENUSE ADJACENT SIDE
ADJACENT SIDE
OPPOSITE SIDE
=
=
=