1. Trigonometry Unit Section 1 Chapter 9

2. What is Trigonometry?  Trigonometry is the study of right triangles.  Two years ago we learned basic trig formulas?

3. Basic Trigonometric Ratios  What is SOH-CAH-TOA ?

4. A Typical Right Triangle

5. More Trig Functions  We have talked about sine, cosine, and tangent.  There are three other functions that are reciprocals of sine, cosine, and tangents. They are called.  Cosecant (csc) csc  =  Secant (sec) sec  =  Cotangent (cot) cot  =

6. Examples  Suppose sin  =  Find csc  ?  Use your calculator to find csc 60?

7. Using Reciprocal Functions to Solve Right Triangles  Csc A =  Sec A = =  Cot A = =

8. Example  When a crane’s boom is elevated to an angle of 70 degrees, it extends to a height of 128ft. How far is the crane’s cab from the point where materials will be dropped?

9. Example  When a crane’s boom is elevated to an angle of 70 degrees, it extends to a height of 128ft. How far is the crane’s cab from the point where materials will be dropped? Tan 70 = 128 x Cot 70 = x 128

10. Special Right Triangles  The following special right triangles help to illustrate the unchanging nature of trigonometric ratios and can be used to remember the basic ratios for 30, 45, and 60 degree angles.

11. Special Right Triangles 45-45-90 Right Triangles The ratios of the sides of all 45-45-90 right triangles are shown in the accompanying drawing. Scalars and/or proportions can be used with these ratios to find the lengths of the sides of any 45-45-90 right triangle if one side is known. 30-30-90 Right Triangles The ratios of the sides of all 30-60-90 right triangles are shown in the accompanying drawing. Scalars and/or proportions can be used with these ratios to find the lengths of the sides of any 30-60-90 right triangle if one side is known.

12. Special Right Triangles Vertex Angle Bisector Conjecture In an isosceles triangle, the bisector of the vertex angle is also the altitude and the median to the base. In an equilateral triangle, the bisector of the vertex angle splits the equilateral triangle into two 30-60-90 right triangles.

13. No Checking For Understanding