R Review Of Prerequisites 1 Functions And Relations 2 Polynomial And Rational Functions 3 Exponential And Logarithmic Functions 4 Trigonometric Functions 5 Analytic Trigonometry 6 Applications Of Trigonometric Functions 7 Trigonometry Applied To Polar Coordinate Systems And Vectors 8 Systems Of Equations And Inequalities 9 Matrices And Determinants And Applications 10 Analytic Geometry 11 Sequences, Series, Induction, And Probability expand_more
5.1 Fundamental Trigonometric Identities 5.2 Sum And Difference Formulas 5.3 Double-angle, Power-reducing, And Half-angle Formulas 5.4 Product-to-sum And Sum-to-product Formulas 5.5 Trigonometric Equations Chapter Questions expand_more
Problem 1SP: Given that sin=45 for in Quadrant II, find the exact function values. a. sin2 b. cos2 c. tan2 Problem 2SP Problem 3SP Problem 4SP: Use the half-angle formula to find the exact value of sin165 . Problem 5SP: Show that 1cos1+cos=sin1+cos. Problem 6SP Problem 1PE Problem 2PE Problem 3PE Problem 4PE Problem 5PE: From the relationship sin2=1cos22, it follows that sinu2 = . Problem 6PE: From the relationship cos2=1+cos22 , it follows that cos u2 = . Problem 7PE: For Exercises 7-14, use the given information to find the exact function values. a.sin2b.cos2c.tan2... Problem 8PE: For Exercises 7-14, use the given information to find the exact function values. a.sin2b.cos2c.tan2... Problem 9PE: For Exercises 7-14, use the given information to find the exact function values. a.sin2b.cos2c.tan2... Problem 10PE: For Exercises 7-14, use the given information to find the exact function values. a.sin2b.cos2c.tan2... Problem 11PE: For Exercises 7-14, use the given information to find the exact function values. a.sin2b.cos2c.tan2... Problem 12PE: For Exercises 7-14, use the given information to find the exact function values. a.sin2b.cos2c.tan2... Problem 13PE: For Exercises 7-14, use the given information to find the exact function values. a.sin2b.cos2c.tan2... Problem 14PE: For Exercises 7-14, use the given information to find the exact function values. a.sin2b.cos2c.tan2... Problem 15PE: For Exercises, 15-20, find the exact value of the expression. 2tan67.51tan267.5 Problem 16PE: For Exercises, 15-20, find the exact value of the expression. 2tan151tan215 Problem 17PE: For Exercises, 15-20, find the exact value of the expression. 2sin12cos12 Problem 18PE: For Exercises, 15-20, find the exact value of the expression. 2sin22.5cos22.5 Problem 19PE: For Exercises, 15-20, find the exact value of the expression. cos28sin28 Problem 20PE: For Exercises, 15-20, find the exact value of the expression. 2cos21651 Problem 21PE Problem 22PE Problem 23PE Problem 24PE Problem 25PE Problem 26PE: For Exercises, 21-34, verify the identity. sin3xsin2x=2cosx12secx Problem 27PE Problem 28PE Problem 29PE Problem 30PE Problem 31PE: For Exercises, 21-34, verify the identity. cos2xsinxsin2xcosx=cscx4sinx Problem 32PE Problem 33PE: For Exercises, 21-34, verify the identity. sin4=4cos3sin4sin3cos Problem 34PE Problem 35PE Problem 36PE Problem 37PE Problem 38PE: For Exercises 39-44, use the half-angle formula to find the exact value. cos4x+sin2x Problem 39PE: For Exercises 39-44, use the half-angle formula to find the exact value. sin165 Problem 40PE: For Exercises 39-44, use the half-angle formula to find the exact value. tan78 Problem 41PE: For Exercises 39-44, use the half-angle formula to find the exact value. cos712 Problem 42PE: For Exercises 39-44, use the half-angle formula to find the exact value. cos112.5 Problem 43PE: For Exercises 39-44, use the half-angle formula to find the exact value. tan75 Problem 44PE: For Exercises 39-44, use the half-angle formula to find the exact value. sin8 Problem 45PE: Fill the table for in the given quadrant, what do you notice about the signs of sin and tan2 ? Problem 46PE: What are the advantages to using the formula tan2=1cossin or tan2=sin1+cos as opposed to... Problem 47PE: For Exercises 47-50, use the given information to find the exact function values. a.sin2b.cos2c.tan2... Problem 48PE: For Exercises 47-50, use the given information to find the exact function values. a.sin2b.cos2c.tan2... Problem 49PE: For Exercises 47-50, use the given information to find the exact function values. a.sin2b.cos2c.tan2... Problem 50PE: For Exercises 47-50, use the given information to find the exact function values. a.sin2b.cos2c.tan2... Problem 51PE: For Exercises 51-56, verify the identity. sin22=csccot2csc Problem 52PE Problem 53PE Problem 54PE Problem 55PE Problem 56PE Problem 57PE Problem 58PE Problem 59PE Problem 60PE Problem 61PE Problem 62PE Problem 63PE Problem 64PE Problem 65PE Problem 66PE Problem 67PE Problem 68PE Problem 69PE Problem 70PE Problem 71PE: For Exercises 71-74, a. Rewrite the function as a single trigonometric function raised to the first... Problem 72PE Problem 73PE: For Exercises 71-74, a. Rewrite the function as a single trigonometric function raised to the first... Problem 74PE: For Exercises 71-74, a. Rewrite the function as a single trigonometric function raised to the first... Problem 75PE Problem 76PE: For Exercises 75-80, find the exact value. cos12arcsin38 Problem 77PE Problem 78PE Problem 79PE Problem 80PE: For Exercises 75-80, find the exact value. tan12cos11517 Problem 81PE Problem 82PE: Find an algebraic expression representing sin2cos1x for 0x1 . Problem 83PE: A feeding trough for cattle is made from a metal sheet 3 ft wide. The sides of the trough are made... Problem 84PE: Consider the triangular area of the roof truss. a. Write the area as a function of sin2 and cos2 .... Problem 85PE: Consider an object launched from an initial height h0 with an initial velocity v0 at an angle from... Problem 86PE: Refer to Exercise 85. Suppose that you kick a soccer ball from ground level with an initial velocity... Problem 87PE: Write cos3x as a third-degree polynomial in cosx . Problem 88PE: Write cos4x as a fourth-degree polynomial incosx . Problem 89PE Problem 90PE Problem 91PE Problem 92PE Problem 93PE Problem 94PE Problem 95PE Problem 96PE Problem 97PE Problem 98PE Problem 99PE Problem 100PE format_list_bulleted