Slide 1

IntroductionThere are six functions that are the core of trigonometry. There are three primary ones.Sine (sin)Cosine (cos)Tangent (tan)The other three are not used as often and can be derived from the three primary functions.Secant (sec)Cosecant (csc)Cotangent (cot)

A-is the length of the sideadjacent to the angle (x) in question.O-is the length of the sideopposite the angle.H-is the length of thehypotenuse.

"x" represents the measure of ther angle in either degrees or radians.

Sinesin x = o/hCosinecos x=a/hTangenttan x=o/a

Cosecantcsc x=h/oCosecantsec x=h/aCotangentcot x=a/o

Solving real life situations of the six trigonometric ratios

LAW OF SINE:You are a woodworker about to cut a triangle out of a piece of wood. You want your bottom side of the triangle to be 7.4 inches. You want the side to the left of the bottom to be 12.5 inches. The angle opposite the bottom side needs to be 36 degrees. What must the angle be opposite the 12.5 side?

36X7.412.5

Solving

SinA/a=sinB/bSin36/7.4=SinA/12.57.4SinA=12.5Sin367.4SinA/7.4=12.5Sin36/7.4SinA=7.35/7.4SinA=Arcsin^AnsSin=81.89

Law of CosineAn aircraft tracking station determines the distance from a common point O to each aircraft and the angle between the aircrafts. If angle O between the two aircrafts is equal to 49o and the distances from point O to the two aircrafts are 50 km and 72 km, find distance d between the two aircrafts. b2= 722+ 502- 2 (72)(50) cos(49o) =5184 + 2500 -7200 cos49 = 7684-4723.63 b2= 2960.37 b=54.40

Law of TangentAt 57" from the base of a building you need to look up at 55 to see the top of a building. What is the height of the building?

tan(55) = height/57 height = 57 tan(55) = 81.4"