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# Trigonometry MAT106

CSU Pomona

GPA 3.53

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This 8 page Class Notes was uploaded by Dr. Elody Harris on Saturday October 3, 2015. The Class Notes belongs to MAT106 at California State Polytechnic University taught by Staff in Fall. Since its upload, it has received 45 views. For similar materials see /class/218206/mat106-california-state-polytechnic-university in Mathematics (M) at California State Polytechnic University.

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Date Created: 10/03/15

Test 2 Review Section 69 Graphs of Other Trigonometric Functions 1 Graph the functions a y tan2x TI TI by cotx Z 2 Graph the functions ay ZSech TI TI by 2cscx 3 Section 71 Basic Trigonometric Identities 3 Use a Pythagorean identity to find the function value indicated a If sin 9 and the terminal side of 6 lies in Quadrant Ill find cos 9 b If cos 9 and the terminal side of 6 lies in Quadrant 11 find csc 9 Section 72 Verifying Trigonometric Identities 4 Verify each of the trigonometric identities 1 a cscx cotx CSCX COtX 1 b 2 csc2 x 1 COSX 1COSX Section 73 Sum and Difference Identities 5 Find the exact value of cosa if cos a g and cos 3 i and the terminal side of 0 lies in Quadrant IV and the terminal side of B lies in Quadrant ll 6 Find the exact value of tana 3 if sin a g and cos 3 i and the terminal side of 0 lies in Quadrant Ill and the terminal side of B lies in Quadrant II Section 74 Double Angle Identities 7 Use the double angle identities to answer the following questions a If secx 2 and sinx gt 0 find tan2x b If sinx and cosx lt 0 find cos2x c If cscx and cosx gt 0 find sin2x 8 Verify the identity 2 1 cos2x 5m x T Section 77 Inverse Trigonometric Functions 9 Find the exact value of each expression 1 5 COS 10 Evaluate each expression exactly sin cos391 3 11 Evaluate exactly a cos sin391 tan391 b tan COS 1 Sin 1 Sections 78 81 82 83 86 87 Review Section 78 Trigonometric Equations 1 Solve the given trigonometric equation exactly on 0 S 9 lt 2n 2 coszx0 2 Solve the given trigonometric equation on 0 3 9 lt 360 2 sinx 1cosx V3 2 0 3 Find all solutions a 2 cos x 1 0 b2cost 3 0 csinx Section 81 Oblique Triangles And The Law Of Sines 4 Solve the given triangle y 100 40 a 16ft Section 82 The Law of Cosines 5 Solve each triangle ab 55 50 20 ba 6 b9c12 Section 83 The Area Of A Triangle 6 Find the area of each triangle described aa 6b 8y 80 ba6b10c9 Section 86 Polar Trigonometricg Form Of Complex Numbers 7 Express each complex number in polar form a 1 N b 0 2i c 2 0i 8 Express each complex number in rectangular form 2cos 135 i sin 135 Section 87 Products Quotients Powers And Roots Of Complex Numbers 9 Find the product 2122 and the quotient 1 2 where 21 4cos 80 isin 80 22 2cos 145 i sin 145 10 Find the result of each expression using DeMoivre s theorem Write the answer in rectangular form 3 3i10 11 Find all complex solutions to the given equations x310 Sections 78 81 82 83 86 87 Review Solutions 1 N0 solution 100 1889568i 2x1150 x230 1111 i1 i 392 2 392 2 3 a x n 21m bx1 1 2kn x2 kn cx1 1 nz2kn x2 21m 40 40 b 16ftc 25ft 5 aa 23 80 y 80 by 104 47 0 29 6 a 236 b 05 7 a 2cos 60 i sin 60 b 2cos 90 i sin 90 c 2cos 180 i sin 180 8 3 NE 9 2122 4 ll i Z1 2cos 65 zsm 65 Zz Test 1 Review Solutions 1711 1611 a T b T E 12 210 b 84 1 3 ft 8 2 762 13W cm 3 14 862 cm2 a 58 a64ftb10ft 154fF b a 62 3 28 a 441 m mm 4 N26 E 16 279 km cm 5 214 miles 17 6 a 6 h 2 18 415 mm I 2 g 19 3665 ft st cch 5 52 20 84 secQ E c056 1 tanQ 2 cote 2 7 h m 6 2m 6 x sm 13 csc 2 6 3m 6 x COS T SEC T t 6 2 t6 3 an 3 co 2 8 I sine 1 I cch 1 I I c056 0 I secQ Undefined I I tanQ 00 I cote 0 12 9 c056 E 10 c056 2 11 Test 1 Review Section 61 Angles Degrees amp Triangles 1 If a 6 foot man casts a 1 foot shadow how long will a shadow will his 4 foot son cast 2 If AB 60 AD 61 and DC 36 nd AC A a Section 63 Solving Right Triangles 3 Solve the right triangle a0t32 andc12ft bb23mandc49m 4 If a plane takes of bearing N33 W and ies 6 miles and then makes a right turn at 90 and ies 10 miles further what hearing will the traffic controller use to locate the plane 5 Two friends who are engineers at Kennedy Space Center KSC watch the shuttle launch Carolyn is at the Vehicle Assembly Building VAB 3 miles from the launch pad and Jackie is across the Banana River which is 8 miles from the launch pad They call each other at liftoff and after 10 seconds they estimate the elevation with respect to the ground Carolyn thinks the elevation is approximately 40 and Jackie thinks the elevation is approximately 15 Approximately how high is the shuttle after 10 seconds 40 15 Section 64 Definition 2 Of Trigonometric Functions 6 The terminal side of an angle 9 in standard position passes through 24 Calculate the values of the six trigonometric functions for angle 7 Calculate the values for the six trigonometric functions of the angle 9 given in standard position if the terminal side of 9 lies on each of the indicated lines 2x3y0x20 8 Calculate the values for the six trigonometric functions of the angle 9 given in standard position 9 450quot Section 65 Trigonometric Functions of Nonacute Angles 9 If tan 6 and the terminal side of 9 lies in Quadrant 11 find the values of the six trigonometric functions of angle 9 10 If cot 6 and the terminal side of 9 lies Quadrant IV find the values of the six trigonometric functions of angle 9 Section 66 Radian Measure amp quot 11 Convert from degrees to radians a 340 b 320 12 Convert from radians to degrees a 7 b Z 13 Find the exact length of the arc made by the indicated central angle and radius of each circle 622 r22cm 14 Find the area of the circular sector given the indicated radius and central angle 6 56 r 42 cm 15 Find the linear speed of a point that moves With constant speed in a circular motion if the point travels along the circle of arc length 3 in time t S 12ftt3min 16 Find the distance traveled arc length of a point that moves With a constant speed v along a circle in time t v 62 kmhr t 45 hr 17 Find the linear speed of a point traveling at a constant speed along the circumference of a circle With radius r and angular speed 1 311 u T radsec r 8 18 Find the distance a point travels along a circle over a time t given the angular speed 1 and radius r of the circle 0 6139 radsec r 2 m t 11 sec 19 The famous clock tower in London has a minute hand that is 14 feet long How long does the tip of the minute hand travel in 25 minutes 20 A smaller gear has a radius of 3 inches and a larger gear has a radius 15 inches If the smaller gear rotates 420 how many degrees has the larger gear rotated Section 68 Graphs of Sine and Cosine Functions 21 Sketch the graphs y 2sinnx 1 andy 4cos2x 7T Test 2 Review Solutions 3 44 C 39E 13 a 8 b151161 1 cos 2x 1 cos2 x sin2 x 161 T 2 4 1 cos2 x sin2 x 2 2 2 a smxsmx251nx 2 2 cscx cotxcscx cotx Sln X cscx cotx cscx cotx o csc2 x cot x 9 150 cscx cotx 1 cot2 x cot2 x 10 g cscx cotx 1 cscx cotx 11 b a 0 1 1 b 1 cosx 1 cos 5 x 1 cosx 1 cosx 1 cos x1 cos x 2 2 1 czos2 x sin2 x 2 csc x 5 12x3 12 6 192 25V 119 7 a 3 3 1

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