December 14th BOOK 4.2 copyright2009merrydavidson

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December 14th BOOK 4.2 copyright2009merrydavidson Happy Birthday to Hira Saleem & Shayna Faith Richardson December 14th BOOK 4.2 copyright2009merrydavidson Factor Completely: 1) 27x3 + 64 2) x4 – 1 3) x2 – xy – 2y2 Simplify: 4) 5) (x+1)(x-1)(x2 + 1) (3x + 4)(9x2 – 12x + 16) (x +y)(x – 2y)

Special Right Triangles S O H C A H T O A

S O H C A H T O A r y Reciprocal functions Parent functions x

Special Right Triangles 30o, 45o, 60o You must memorize these!!! 60o The x-value is the cosine of that angle. The y-value is the sine of that angle. Use the pythagorean theorem to find the sides.

Paper Plates Label co-ordinates on your plate by each special angle. (cosine, sine) Be careful with + and – signs.

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

Practice….. negative positive negative Would the cosine of a -120o angle be positive or negative? Would the cotangent of an 82o angle be positive or negative? Would the secant of a -98o angle be positive or negative? negative positive negative

Evaluating Trig Functions: Use your Plate, 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 Plate, find the angle, evaluate. Rationalize the denominator as needed. 1: Find the six trig. values for -5/4. sin = csc = cos = sec = tan = cot =

Find the sine of the angles listed. 30o = 390o = -330o = What is the NAME of the type of these 3 angles? co-terminal angles What conclusion can you make? Co-terminal angles have the same trig values. It takes 360o to get to the same trig value, thus the PERIOD for the sine and cosecant function is 360o.

Find the cosine of the angles listed. 60o = 420o = -300o = It takes 360o to get to the same place, thus the PERIOD for the cosine and secant function is 360o.

Find the tangent of the angles listed. 45o = 225o = -135o = It takes 180o to get the same trig value, thus the PERIOD for the tangent and cotangent function is 180o.

sin/csc/cos/sec have a period of 360o. Summary of Period sin/csc/cos/sec have a period of 360o. tan/cot have a period of 1800. BE CAREFUL TO NOT USE CAPITAL LETTERS. WE WILL LEARN THAT LATER

HW: WS 6-3