1.3 Definition 1 of Trigonometric Functions

1. 1.3 Definition 1 of Trigonometric Functions JMerrill, 2009

2. Trigonometry • The word trigonometry comes from two Greek words, trigon and metron, meaning “triangle measurement”. We will “measure” triangles by concentrating on their angles. • Definition 1 ONLY works for right triangles

3. Trigonometric Functions (Ratios) • There are six trigonometric functions: • Sine abbreviated sin--sinθ • Cosine abbreviated cos--cosθ • Tangent abbreviated tan--tanθ • Cosecant abbreviated csc--cscθ • Secant abbreviated sec--secθ • Cotangent abbreviated cot--cotθ

4. Recall from 1.2 • We discussed the ratios of the sides of similar triangles • The three main trigonometric functions should be learned in terms of the ratios of the sides of a triangle.

5. Right Triangle Trig SOH-CAH-TOA • Sin θ = • Cos θ = • Tan θ = • These are the ratios of 2 sides with respect to an angle. • In order to find the other trig functions, we must look at some identities hypotenuse opposite θ adjacent

6. Fundamental Trigonometric Identities Reciprocal Identities Also true:

7. Example • Find the following—exact answers only D 4 5 Sin D = Sin G = Cos D =Cos G = O 3 G Tan D = Tan G = Board Example

8. Cofunctions • Notice the co in cosine, cosecant, and cotangent. These are cofunctions and they are based on the relationship of complementary angles. • The Cofunction Theorem states that if α+β = 90o, then: sin β = cos α sec β = csc α tan β = cot α

9. Cofunction Examples • Sin 30o = • Csc 40o = • Tan x = Cos 60o Sec 50o Cot (90o-x)

10. Fundamental Trigonometric Identities Cofunction Identities