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1 Algebra 3 Assignment Sheet (1) Assignment # 1 Complete the circle diagram (2) Assignment # 2 Sine & Cosine functions chart (3) Assignment # 3 Other Trig functions chart (4) Assignment # 4 Finding other trig functions (5) Assignment # 5 Review Worksheet (6) TEST (7) Assignment # 6 Angle Addition Formulas (8) Assignment # 7 Double, Half-Angle Formulas (9) Assignment # 8 Review Worksheet (10) TEST (11) Assignment # 9 Problems ( 1 – 9 ) Solving Trig Equations (12) Assignment # 9 Problems ( 10 – 18 ) Solving Trig Equations (13) Assignment # 10 Review Worksheet – Solving Trig Equations (14) TEST (15) Assignment # 11 Problems ( 1 – 6 ) Graphing Sine and Cosine functions (16) Assignment # 11 Problems ( 7 – 12 ) Graphing Tangent and Cotangent functions (17) Assignment # 11 Problems ( 13 – 18 ) Graphing Secant and Cosecant functions (18) Assignment # 12 Review Worksheet – Graphing Trig Functions (19) TEST 2 INTRODUCTION TO TRIGONOMETRY I Definition of radian: Radians are an angular measurement. One radian is the measure of a central angle of a circle that is subtended by an arc whose length is equal to the radius of the circle. 10 Therefore: 5 1 arc length = angle in radians x radius 2R R 5 5 r The radius wraps itself around the circle 2 times. Approx. 6.28 times. Therefore 360 = 2 R 1 rad r 2 R R Dividing you get 1 ……….. 1 360 180 180 Conversely ………………………... 1R R 2 Ex. Change 60 to radians. 60 3 180 R Change 3 2 Convert the following from degrees to radians or vice versa: 1. 36 2. 320 4. 15 5. 17 20 4 to degrees. 180 45 4 R 0 R , 2 R 3. 195 0 6. 5 3 3 II UNIT CIRCLE: The unit circle is the circle with radius = 1, center is located at the origin. What is the equation of this circle? Important Terms: A. Initial side: B. Terminal side: C. Coterminal angles: D. Reference angles: The initial and terminal sides form an angle at the center if the terminal side rotates CCW, the angle is positive if the terminal side rotates CW, the angle is negative unit circle positive negative Coterminal angles have the same terminal side…. -45˚ and 315˚ or coterminal 7 and 3 3 The reference angle is the acute angle made between the Terminal Side and the x-axis 4 III GEOMETRY REVIEW 30 – 60 – 90 RIGHT TRIANGLES 45 – 45 - 90 45 60 2a a a 2 a 45 30 a a 3 45 60 2 2 1 30 1 45 3 1 5 Algebra 3 Assignment # 1 6 Trigonometric Functions Let θ “theta” represent the measure of the reference angle. Three basic functions are sine, cosine and tangent. They are written as sin θ, cos θ, and tan θ Right triangle trigonometry - SOHCAHTOA sin opp hyp cos adj hyp tan opp adj hyp opp θ adj A. Find cos θ B. Find sin θ 5 2 12 θ θ 5 13 5 3 5 C. Find tan θ D. Find sin θ 25 9 6 θ θ 7 7 Triangles in the Unit Circle B (0,1) P(x,y) I 1 y + O x A (1,0) + + + _ + O _ _ + + x2 y 2 1 y y 1 x cosθ x 1 y tanθ x sinθ II Reference Triangles Where functions are positive S A T C S A T C A. Drop from point to x-axis. 8 B. Examples 3 1. Find the sin 4 coterminal angles 2. Find the cos 4 Same as cos R 4 3 5 coterminal angles 3. Find the sin 420 = coterminal angles 13 4. Find the cos 6 = 9 III Quadrangle Angles Def: An angle that has its terminal side on one of the coordinate axes. To find these angles , use the chart B (0,1) y y 1 x cosθ x 1 y sin tanθ x cos sinθ C (-1,0) A (1,0) D (0,-1) Find the sine and cosine for all the quadrangles. 0 0 R 90 R 2 sin 0 cos 0 sin cos 180 R sin cos 3 270 R 2 sin cos 360 2 R sin cos Trig values 10 Algebra 3 Assignment # 2 Complete each of the following tables please. Radian Measure 11 3 Degree Measure 5 4 330 19 6 3 45 450 210 Sin Cos Radian Measure Degree Measure Sin Cos 3 2 180 7 3 4 150 11 4 780 90 11 Answers Radian Measure 11 3 11 6 5 4 5 2 19 6 4 3 Degree Measure 660 330 225 450 570 45 540 210 3 2 1 2 1 0 1 2 Sin Cos 1 2 3 2 3 2 Degree Measure 270 180 Sin 1 0 Cos 0 1 Radian Measure 2 2 2 2 0 1 2 3 2 2 2 2 2 1 7 6 3 2 7 3 5 6 4 13 3 11 4 2 420 150 45 780 495 90 3 2 1 2 1 2 2 2 2 2 3 2 1 2 2 2 2 2 3 2 1 0 12 6.2 Other Trigonometric Functions Sin Cosecant: Cos Secant: Tan Cotangent: http://mathplotter.lawrenceville.org/mathplotter/mathPage/trig.htm Find the following values 1. csc 5. tan 4 4 3 2. cot 6 6. cot 4 3. sec2 4. sec 3 2 7. csc 3 8. tan 17 6 13 6.2 Algebra 3 Assignment # 3 Complete the following tables. 8 3 Radian Measure Degree Measure 6 3 4 330 5 135 450 240 Sin Cos Tan Cot Sec Csc Radian Measure Degree Measure Sin Cos Tan Cot Sec Csc 3 2 540 7 3 13 4 150 7 4 210 270 Alg 3(11) Ch 6 Trig 14 Answers Radian Measure Degree Measure Sin Cos 8 3 11 6 3 4 5 2 6 480 330 135 450 30 3 2 1 2 1 2 3 2 1 3 2 2 2 2 1 Undef. 3 1 0 Tan 3 Cot 1 3 1 2 3 2 1 0 135 1 3 1 Undef. 1 3 Undef. 2 3 2 1 2 2 Undef. 2 3 2 2 1 2 3 2 3 7 3 5 6 13 4 420 150 585 210 3 2 1 2 1 2 2 2 2 2 1 2 Sin 1 0 Cos 0 1 Tan Undef. 0 Cot 0 Undef. Sec Undef. 1 Csc 1 Undef. 3 3 2 1 3 1 3 3 2 2 3 1 3 2 1 2 3 Csc 540 0 0 2 270 240 1 3 2 3 900 2 2 2 2 2 4 3 Sec Radian Measure Degree Measure 5 3 4 1 2 3 2 2 2 2 3 7 4 3 2 315 270 2 2 2 2 1 1 Undef. 3 1 0 2 3 2 Undef. 1 7 6 3 2 1 3 2 2 0 1 Alg 3(11) Ch 6 Trig 15 6.2 MORE TRIG FUNCTIONS Identifying in which quadrant the angle lies is essential for having the correct signs of the trig functions. If given, Sin θ = 3 and if told that 0 , can we find the cos θ? 2 5 1 θ θ 3/5 θ x 1. Find cos if sin = 2/3 and 0 2 2. Find tan if sin = 3/7 and 2 Alg 3(11) Ch 6 Trig 16 3. Find csc if cos = 5. If Tan = - 3 3 and 2 2 4. Find sec if sin = -1/3 and 3 2 2 4 , 270 θ<360 , find all the remaining functions of . 5 6. Find the values of the six trig. functions of , if is an angle in standard position with the point (-5, -12) on its terminal ray. Alg 3(11) Ch 6 Trig 17 Algebra 3 Assignment # 4 (1) Sin( ) = 3 , 0 < < . Find the remaining 5 trig. functions of . 2 5 (2) Cos( ) = 4 , < < . Find the remaining 5 trig. functions of . 5 2 (3) Tan( ) = 12 , < < 3 . Find the remaining 5 trig. functions of . 2 5 (4) Sec( ) = 7 3 , < < 2 . Find the remaining 5 trig. functions of . 5 2 (5) Csc( ) = 7 , 180 < < 270 . Find the remaining 5 trig. functions of . 3 (6) Cot( ) = 2 , 270 < < 360 . Find the remaining 5 trig. functions of . (7) Sin( ) = 24 , 180 < < 270 . Find the remaining 5 trig. functions of . 25 (8) Find the values of the six trig. functions of , if is an angle in standard position with the point (4 , 3) on its terminal ray (9) Find the values of the six trig. functions of , if is an angle in standard position with the point (5 , 12) on its terminal ray Alg 3(11) Ch 6 Trig 18 Trig Assignment #4 Answers (1) cos( ) = 4 , tan( ) = 3 , cot( ) = 4 , sec( ) = 5 , csc( ) = 5 5 4 3 4 3 (2) sin( ) = 3 , tan( ) = 3 , cot( ) = 4 , sec( ) = 5 , csc( ) = 5 5 4 3 4 3 (3) sin( ) = 12 , cos( ) = 5 , cot( ) = 5 , sec( ) = 13 , csc( ) = 13 13 13 5 12 12 (4) sin( ) = 2 6 2 6 , cos( ) = 5 , tan( ) = , cot( ) = 5 , csc( ) = 7 7 7 5 2 6 2 6 (5) sin( ) = 3 , cos( ) = 7 (6) sin( ) = 1 , cos( ) = 5 7 2 10 2 10 , tan( ) = 3 , cot( ) = , sec( ) = 7 3 2 10 2 10 2 , tan( ) = 1 , sec( ) = 2 5 5 , csc( ) = 5 2 (7) cos( ) = 7 , tan( ) = 24 , cot( ) = 7 , sec( ) = 25 , csc( ) = 25 7 24 25 7 24 (8) sin( ) = 3 cos( ) = 4 , tan( ) = 3 , cot( ) = 4 , sec( ) = 5 , csc( ) = 5 5 4 3 3 5 4 (9)sin( ) = 12 cos( ) = 5 , tan( ) = 12 , cot( ) = 5 , sec( ) = 13 , csc( ) = 13 5 12 13 13 5 12 Alg 3(11) Ch 6 Trig 19 Algebra 3 Review Worksheet (1) Complete the following table please. Rad. Deg. 2 3 3 2 135 330 150 9 10 3 3 4 750 4 240 sin cos tan cot sec csc (2) Sin(x) = 5 , x . Find the remaining 5 trig functions of x. 2 7 (3) Tan() = 1 , 0 90 . Find the remaining 5 trig functions of . 2 (4) Cot(x) = 0.8 , x 3 . Find the remaining 5 trig functions of x. 2 (5) Sec() = 3 , 90 180 . Find the remaining 5 trig functions of . (6) Find the values of the six trig. functions of , if is an angle in standard position with the point (5 , 3) on its terminal ray. Alg 3(11) Ch 6 Trig 20 Algebra 3 Review Answers (1) 2 3 3 4 3 2 11 6 3 5 10 3 25 9 4 3 Deg. 120 135 270 330 540 150 600 750 405 240 45 sin 3 2 2 2 1 1 0 1 1 2 2 cos 1 2 2 0 1 tan 3 1 Undef 3 2 1 3 cot 1 1 0 3 Undef sec 2 2 Undef 2 3 csc 2 3 2 1 2 Rad. 2 3 2 6 2 3 2 1 3 6 3 2 2 1 4 3 2 2 2 2 2 1 2 2 2 1 3 1 1 1 3 1 2 2 3 3 2 1 3 3 1 3 3 1 2 3 2 2 3 2 Undef 2 2 3 2 2 0 2 2 3 (2) cos(x) = 2 6 , tan(x) = 5 , cot(x) = 2 6 , sec(x) = 7 , csc(x) = 7 7 (3) sin() = 1 5 2 6 , cos() = 2 , cot() = 2 , sec() = 5 5 5 2 6 5 , csc() = 2 5 (4) sin(x) = 5 , cos(x) = 4 , tan(x) = 5 , sec(x) = 41 , csc(x) = 41 41 41 4 4 (5) sin() = 2 2 , cos() = 1 , tan() = 2 2 , cot() = 1 3 (6) sin() = 34 3 3 2 2 4 5 , csc() = 3 2 2 3 , cos() = 5 , tan() = 3 , cot() = 5 , sec() = 34 , csc() = 5 3 5 34 34 2