Homework 4 Chapter 6 - Berkeley City College

Berkeley City CollegeHomework Due:_______________________Precalculus - Math 1 - Chapter 6 Introduction to TrigonometryName___________________________________Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measureof two other angles, one positive and one negative, coterminal with the given angle.1) 50° 1)Evaluate the expression.2) tan(-180°) 2)3) sin 450° 3)4) sin(-90°) 4)5) cos 0° - 9 sin 90° 5)6) 6 tan 0° + 3 csc 270° 6)Instructor: K. Pernell 1

Suppose that θ is in standard position and the given point is on the terminal side of θ. Give the exact value of theindicated trig function for θ.7) (6, 8); Find sin θ. 7)8) (-15, 36); Find sin θ. 8)9) (-7, 5); Find tan θ. 9)Sketch an angle θ in standard position such that θ has the smallest positive measure and the given point is on theterminal side of θ.10) (-2, 5)10)yxIdentify the quadrant for the angle θ satisfying the following conditions.11) tan θ > 0 and sin θ < 0 11)2

12) sin θ > 0 and cos θ < 0 12)13) cot θ < 0 and cos θ > 0 13)Determine the signs of the given trigonometric functions of an angle in standard position with the given measure.14) cos (-280°) and sin (-280°) 14)15) csc (569°) and cot (569°) 15)Use the fundamental identities to find the value of the trigonometric function.16) Find sin θ, given that cos θ = 2 3and θ is in quadrant IV. 16)17) Find sec θ, given that tan θ = 3 4and θ is in quadrant I. 17)18) Find sin θ, given that cos θ = 4 7and tan θ < 0. 18)3

19) Find csc θ, given that cot θ = - 5 and cos θ < 0. 19)4Solve the problem.20) Find the exact value of x in the figure.20)2221) Find the exact value of x in the figure.21)20x4

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side lengthusing the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle.Rationalize the denominator if applicable.22) Find sin A when b = 30 and c = 50 22)23) Find tan B when a = 48 and c = 50. 23)Find all values of θ, if θ is in the interval [0, 360°) and has the given function value.24) cos θ = 1 224)25) sin θ =3225)Give the exact value.26) cos 150° 26)27) tan 120° 27)28) cot 300° 28)5

29) sec 210° 29)30) csc 210° 30)Find the exact trigonometric function value.31) sin (-300°) 31)32) cos 2640° 32)Find the reference angle for the given angle.33) 79° 33)34) 171° 34)35) 202.0° 35)6

36) -445° 36)Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression.37) csc x(sin x + cos x) 37)38)csc x cot xsec x38)Factor the trigonometric expression and simplify.39) 1 - 2 sin2x + sin4x 39)40) sin2x + sin2x cot2x 40)Perform the indicated operations and simplify the result.sin θ41)1 + sin θ - sin θ1 - sin θ41)42) sin θcos θ + cos θsin θ42)7

Use the fundamental identities to simplify the expression.csc θ cot θ43)sec θ43)Find the area of triangle ABC with the given parts.44) A = 37.3°b = 10.7 inc = 6.8 in44)8

Answer KeyTestname: 13SPR_M1_CH6_PROBS1) 410° and -310°2) 03) 14) -15) -86) -37) 4 58) 12139) - 5 710)11) Quadrant III12) Quadrant II13) Quadrant IV14) positive and positive15) negative and positive16) -5317) 5 418) -19)41433720) 11 321) 20 6322) 4 59

Answer KeyTestname: 13SPR_M1_CH6_PROBS723)2424) 60° and 300°25) 60° and 120°26) -3227) - 328) -3329) - 2 3330) -231)3232) - 1 233) 79°34) 9°35) 22°36) 85°37) 1 + cot x38) cot2 x39) cos4x40) 141) -2 tan2θ42) sec θ csc θ43) cot2θ44) 22 in210