January 20 th BOOK 4.2 copyright2009merrydavidson

All Students Take Classes Determine in which quadrant each trig function is positive. QI: All QII: sin/csc QIII: tan/cot QIV: cos/sec

Trig Identities f(x) = cos xf(x) = sin x EVEN ODD

Trig Identities f(x) = tan x ODD

Practice… Follow the correct order of operations. 1.Find sin 180  (a quandrantal angle) 2.Find 3 cot 7  /6 3.Find tan 120  + cot (-30  ) 4.csc  /2 sin  /2 0 3(cos/sin) =

Practice… 5) If cos (-t) = -1/5, a) find cos (t)b) find sec (-t) -1/5 -5

Given 1 trig function, find the value of the remaining 5. 6) sin (t) = ¼, find the remaining values. Step 1: ¼ is positive so draw a right triangle in quadrant I because sine is positive in quadrant 1. Step 2: Label opposite and hypotenuse. 1 4 Step 3: Use pythagorean Thm. To find the missing side. Step 4: Use sohcahtoa to find the missing trig values. Be sure to rationalize the denominator when necessary. t

sin t = csc t = cos t = sec t = tan t =cot t =

Given 1 trig function, find the value of the remaining 5. 7) tan (t) = 2/5; find the remaining values. Step 1: 2/5 is positive so draw a right triangle in quadrant I because tangent in positive in QI. Step 2: Label opposite and adjacent. 2 5 Step 3: Use pythagorean Thm. To find the missing side. Step 4: Use sohcahtoa to find the missing trig values. t

sin t = csc t = cos t = sec t = tan t =cot t =

EX 8: The terminal side of an angle with measure  in standard position passes through (4,-5). Sketch the reference angle. Evaluate sin , cos , and cot .  (4,-5) Step 1: draw what you know Step 2: Find the hypotenuse. Step 3: Use SOHCAHTOA to find what is asked. sin  = -5 / 41 cos  = 4 /41 cot  = -4/5

EX 9: Terminal side of an angle with measure , in standard position, ending at (-4,7). Evaluate all six trig functions.

EX 10:  is given in standard position in QII and sin  = 2/7, find cos , tan , and sec . In QII the x value is NEGATIVE

EX 11:  is in standard position in quadrant III, and tan  = 2/5. Find sin , csc  and cot . In QIII the x value and y value’s are NEGATIVE! The radius is ALWAYS positive.

Quiz Monday over: Fill in a blank unit circle with everything. Give the (x,y) ordered pairs for specific radian values. Give the sine/cosine at certain radian values. Given a specific trig value, find the other 5 trig values. Given a point on the terminal side of an angle, find the 6 trig functions. Know which trig functions are even and odd. Know the period for all 6 trig functions. Given a right triangle, find 2 of the sides and/or 2 of the angles using SOHCAHTOA. Answer 2 application problems using SOHCAHTOA.

HW: WS 6-6 study for quiz