Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Section 5.2 Trigonometric Functions of Real Numbers Definition of the Trig Functions Let t be any real number and let P(x, y) be the terminal point on the unit circle determined by t. Then: sin t = y cos t = x tan t = (x ≠0) y x x 1 1 y y csc t = (y x ≠0)cot t = (y ≠0) ≠0) sec t = (x Oct 57:24 AM 1 sinx cosx sinx cosx tanx tanx sinx 0 cscx cscx secx secx cotx cotx Nov 308:48 AM 2 Domains of the Trig Functions FunctionDomain sin, cos All real numbers tan, sec All real numbers other than + n π π 2 cot, csc All real numbers other than n π Signs of the Trig Functions Oct 83:05 PM 3 EvenOdd Properties sin, csc, tan and cot are odd functions; cos and sec are even functions sin(t) = sin t cos(t) = cos t csc(t) = csc t sec(t) = sec t tan(t) = tan t cot(t) = cot t Oct 96:38 AM 4 Find the sign of the expression if the terminal point determined by t is in the given quadrant. tan(t)csc(t) in quadrant II From info. given, find the quadrant in which the terminal point determined by t lies: cos (t) < 0 and cot (t) < 0 Dec 58:33 AM 5 Fundamental Identities Reciprocal Identities csc t = sec t = 1 cos t 1 sin t sin t tan t = cos t cot t = cot t = 1 tan t cos t sin t Pythagorean Identities sin2 t + cos2 t = 1 tan2 t + 1 = sec 2 t 1 + cot2 t = csc2 t Oct 96:41 AM 6 Using the calculator to find trig values Using Remember: 1. If the rotation is given in radians your calculator must be set to radian mode 2. To find the csc, sec or cot you must calculate ________1_______ the appropriate reciprocal function Dec 37:08 AM 7