Introduction to Engineering Technology Seventh Edition Robert J. Pond & Jeffery L. Rankinen

1. Introduction to Engineering TechnologySeventh EditionRobert 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” 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. B c a A b

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 “sohcahtoa” a _ c B = c b_ c = a 90o q a _ b = A b 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.

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) = 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 = = =

6. Trig Example Find the total impedance, ZT, 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 – 36.87o To find ZT , Use the Pythagorean Theorem a2 + b2 = c2 42 + (-3) 2 = c2 16 + 9 = 25 √25 = c2 5 = c = ZT