Trigonometric Functions: The Unit Circle Section 4.2
Objectives I can list the 6 trig functions I can find the key values of any of the trig functions on the Unit circle I can identify the period of each trig function I can identify which trig functions are even or odd
6 Trig Functions Cosine (cos) Sine (sin) Tangent (tan) Secant (sec) Cosecant (csc) Cotangent (cot) Which ones are related as reciprocals??
S O H - C A H - T O A Parent functions Reciprocal functions
Reciprocal Identities
Quotient Identities
We get cosine and sine values for angles from the unit circle We get cosine and sine values for angles from the unit circle. We get the rest from SOH-CAH-TOA and reciprocals
Evaluating Trig Functions: Use your unit circle, find the angle, evaluate. Rationalize the denominator as needed. 1: Find the six trig. values for 300. sin 300o = csc 300o = cos 300o = sec 300o = tan 300o = cot 300o =
Evaluating Trig Functions: Use your unit circle, find the angle, evaluate. Rationalize the denominator as needed. 1: Find the six trig. values for -5π/4 sin = csc = cos = sec = tan = cot =
Even and Odd Trigonometric Functions The cosine and secant functions are EVEN. cos(-t) = cos t sec(-t) = sec t The sine, cosecant, tangent, and cotangent functions are ODD. sin(-t) = -sin t csc(-t) = -csc t tan(-t) = -tan t cot(-t) = -cot t
Trig Properties f(x) = cos x f(x) = sin x EVEN ODD
sin(-t) = -sin t
cos(-t) = cos(t)
Problems -1/4 If sin (t) is 3/8, then csc (t) = 8/3. If sin (t) = ¼, find sin (-t). If sin (t) is 3/8, find csc (-t). 3) If cos (t) = -3/4, find cos(-t). -1/4 If sin (t) is 3/8, then csc (t) = 8/3. We want to find csc (-t) which is the opposite of csc (t) = -8/3. cos(t) = cos(-t) so = -3/4
Definition of a Periodic Function A function f is periodic if there exists a positive number p such that f(t + p) = f(t) For all t in the domain of f. The smallest number p for which f is periodic is called the period of f.
Function Period (Radians) Period (Degrees) Cosine 2π 360° Sine Secant Cosecant Tangent π 180° Cotangent
Homework WS 8-7