Chapter 4-4: Sin, Cos, and Tan Identities

Pythagorean Identity: Basic Equation of a Circle: Applying what we learned in 4-3: Correct Notation: Unit Circle Connection: 1 Cos θ Sin θ What relationship did you learn about the sides in a right triangle???

Application of Identity: If cos θ = 4/5, find sin θ: Let’s use the identity: So, sin θ = ±3/5 Q: Why are their two correct answers? Let’s look at the circle…. Where is the Cos positive? And what do we know about the s-i-g-n of the Sin in those two quadrants? So: Unless you know which quadrant you started in, there should be two answers to questions like these. ✓ ✓

The Rest of the Theorems: You don’t need ANY names You don’t need ANY of the Theorems themselves Just ask yourself the following two questions: 1)Where am I in the circle? 2)How does the s-i-g-n compare to where I am going in the circle?

Application of the Theorems you don’t need to know: 1)Where am I in the circle? 2)How does the s-i-g-n compare to where I am going in the circle? Examples: -If cos θ =.34, find cos(- θ) -If tan (- θ ) = 5, find tan θ -If sin θ =.8, find sin(π + θ) -If cos θ = 1/2, find cos(π + θ) -If tan θ = 4.7, find tan(π - θ) -If sin (θ ) = 5, find sin(π - θ)

Application of the Theorems you don’t need to know: Examples: -If cos θ = -.364, find sin(π/2 - θ) -If tan θ = -1/3, find tan(π/2 - θ) -If sin θ = 2/5, find cos(π/2 - θ) Let’s review some basic right triangle trig: Sin = Cos = Tan = Soh-Cah-Toa