1. INTRODUCTION TO ENGINEERING TECHNOLOGY SEVENTH EDITION ROBERT J. POND & JEFFERY L. RANKINEN CHAPTER 6 RIGHT-TRIANGLE TRIGONOMETRY AND GEOMETRY FOR TECHNOLOGISTS

2. RIGHT-TRIANGLE RELATIONSHIPS 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.

3. RIGHT-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 ► Three angles always total 180º ► For a right triangle, angles A and B total 90º ► 2 angles that add to 90º are called complementary

4. TRIGONOMETRIC FUNCTIONS a _ c = = b_ c = a _ b c a b  90 o 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

5. 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) = 30 o THE COSECANT, SECANT, AND COTANGENT FUNCTIONS ARE RECIPROCALS OF THE SINE, COSINE AND TANGENT FUNCTIONS HYPOTENUSE OPPOSITE SIDE HYPOTENUSE ADJACENT SIDE OPPOSITE SIDE = = =

6. TRIG EXAMPLE FIND THE TOTAL IMPEDANCE, Z T, AND THE ANGLE, Θ, OF THE AC CIRCUIT BELOW. Tan A = opp = -3/4= - 0.75 adj Use inv Tan or Tan -1 to find angle measurement of – 36.87 o To find Z T, Use the Pythagorean Theorem a 2 + b 2 = c 2 4 2 + (-3) 2 = c 2 16 + 9 = 25 √25 = c 2 5 = c = Z T