MIDTERM 1 MATH 1021
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This 4 page Study Guide was uploaded by mia on Thursday March 3, 2016. The Study Guide belongs to MATH 1021 at University of Colorado taught by rachel benefiel in Winter 2016. Since its upload, it has received 90 views. For similar materials see Pre-calculas Trigonometry in Applied Mathematics at University of Colorado.
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Date Created: 03/03/16
Trigonometry midterm study guide CHAPTER 1: 1.1: ANGLE BASICS <ABC (B=vertex) -Counterclockwise=positive measurement -Clockwise=negative measurement -Measuring angles: degrees, min, sec decimal degrees Ex: 67 °(degrees) 42’(min) 10’’(sec) 67° 42’/60=. 7 10’’/3600=. 002 ANSWER: 67.702° -TYPES of angles: -Obtuse -Acute -Complementary/supplementary angle -Standard position -coterminal -Angle relations -Congruent -Similar 1.3/1.4 -Sin: sinθ: cosecant: csc θ (1/y) -cos: cos θ secant: secθ (1/x) SOH CAH TOA -tan: tan θ cotangent: cot θ (x/y) Pythagorean identity: sinº θ +cosº θ =1 Tanº θ +1=secº θ 1+cot θ =cscº θ FILL IN THE MISSING SPACES:***memorize*** θ Sin Cos Tan Cot Sec csc 0 0 1 0 DNE 1 DNE 90 1 180 0 1 0 1 DNE 270 360 0 0 DNE DNE Quadrant Sin(csc) Cos(sec) Tan(cot) 1 + + + 2 + - - 3 - - + 4 - + - CHAPTER 2: o 2.1: ACUTE TRIANGLES aº+bº=cº -30/60/90 triangle: sin60°=√3/2 sin30°=1/2 cos60°=1/2cos30°=√3/2 tan60°=√3 tan30°=√3/3 -45/45/90: sin45°=√2/2 cos45°=√2/2 tan45°=1 o 2.2 NON ACUTE TRIANGLES (not in Q1) *Reference angle ALWAYS in Quadrant 1!!! o 2.3 ANGLE OF ELEVATION/DEPRESION o 2.4 BEARING *starting due North CHAPTER 3: 3.1 ANGLE MEASURES 360=2π degrees radians 180=π (x°)(π/180) 90=π/2 60=π/3 radians degrees 45=π/4 (radian)(180/π) 30=π/6 Ex: sin π/6=1/2(y-value on the UNIT CIRCLE) ***MEMORIZE the unit circle*** 3.2 ARC LENGTH s=r θ , θ in radians; r=radius; s=arc length A=1/2 rº θ , θ in radians Sin=y cos=x tan=y/x Csc=1/y sec=1/x cot=x/y 3.3 UNIT CIRCLE**** MEMORIZE CHAPTER 4: 4.1 PERIODIC FUNCTIONS -Functions that repeat over some interval size of interval = period Graph of : sinx(period=2π) Cosx(period=2π) *normal periods* Tanx(period=π) A sin X -A= amplitude: always positive, highest distance of baseline (-)sin(bx) b helps find period- period=regular period/b Negative (-) in front means flip the graph 4.2 -Vertical shift sinx+3 shift up 3 units -Phase shift sin(x+2) if positive shifts left; if negative shifts right *If period shifts, it affects the phase shift (horizontal shift) A sin/cos (Bx+C) +D -A = Amplitude(step 3) -B =period 2π/b(step 1) -C =phase shift C/B(step 2) -D = vertical shift(step 4) 4.3 - Know graphs for: TAN, COT SEC, CSC Can find vertical asymptotes when ever dividing by zero -ie: tan @ π/2 cot @ π SUMMARY OF WORKSHEETS #1 -parabola translations f(x)+2 (up 2 units) 2f(x) = divide by 2) f(x+2) =left 2 units -1/2f(x) = divide by ½ (or multiply by 2) -find points on graph where f(x) = y value #2 given terminal angle and find +/- coterminal angles ie:θ -360= AND θ +360= -decimal degrees degrees/min/sec multiply by 60 ex: 120.5 (.5)(60)= 30.00 (.00)(60) = . 00 120° 30’ 00’’ -standard position: vertex at origin and initial side along x-axis *Find both +/- x°(clockwise/counterclockwise) -distance formula: √(x2-x1)º+(y2-y1)º -similar triangles/angles(cross multiply) #3 sin = y/r cos = x/r tan = y/x csc = r/y sec = r/x cot =x/y #4 SOH CAH TOA -Reciprocal identities -Quotient identities -Pythagorean identities #5 inside triangle =180° #6 reference angles : ie: 293° (360°-293°) =67° θ Sin Cos Tan Sec Csc cot 30 1/2 2 45 √2/2 1 √2 60 1/2 2√3/3 √3/3 #7 reciprocal if sin/cos/tan finds the angles #8 bearing/ angle of elevation and solving triangles #9 degrees radians : radians degrees #10 s=r θ , θ in radians; A=1/2 rº θ , θ in radians #11 UNIT CIRCLE helps to recognize decimals and put into π form -1/2=.5 -√3=1.73 -√2=1.414 -2√3/3=1.1546 - be able to find where sin s = ½ in [π/2, π) =150° #12 Y= A sin (Bx+C)+D -know normal periods and graphs -be familiar with the quiz material
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