Math 151      Study Guide for Hour Quiz #5       C.S.Davis

 

You are responsible for the subject matter in the sections below. The following topics are the most important. Typical exercises from Precalculus, 4rd edition, by Stewart, Redlin & Watson are assigned at the end of each objective. Work additional exercises if you need more practice. The answers to the odd numbered problems are in the back of the text.  These exercises are for practice and are not graded.  The problem sets found on the PreCalculus Welcome Page are graded in class.  See the Semester Plan for the current dates for the grading of the problem sets and taking of the hour quizzes.

7.1          Trig expressions have so many forms in calculus; we need to tell when they are equal.        
1. Prove trigonometric identities.   P533#25-39 odd
7.2          The prefix "co" in "cofunctions" refers to trig functions of complementary angles.
1 Use addition and subtraction formulas for sine, cosine and tangent.   P539#1-15 odd
2. Explain the meaning of cofunction.   P539#19,21
3. Prove trig identities involving addition and subtraction formulas.   P540#31,33
7.3          Double and half angle formulas play a large roll in integration techniques in calculus.
1. Use double angle formulas for sine, cosine and tangent.   P548#1,3
2. Use formulas for lowering powers (sometimes called half angle identities)   P548#9,13
3. Use half angle formulas for sine, cosine and tangent.   P548#15,23,27,29,35,37
4. Prove identities involving double angle and half angle formulas.    P548#59,61,63
7.4          Calculus deals with rates of change of functions, including inverse trig functions.
1. Give the domain and range and graphs of inverse trig functions.   text
2. Write what each trig function "means" and find its value exactly.   P557#1,3,5,7
3. Find values of inverse trig function by calculator.   P557#9
4. Find the exact values of compositions of trig and inverse trig functions.   P557#13,17,23,25,27,29,31
5. Rewrite expressions involving inverse functions as an algebraic expression in the independent variable x.   P558#41,43,45,47
7.5          Solving equations, including trig equations, is at the heart of mathematics.
1. Solve trigonometric equations.   P568#3,9,19,23,41,47,53,57,61,65
9.1          Telescopes and highways are designed using parabolas.
1. Given one specification of a parabola, determine any of the others: equation, graph, focus & directrix, focus & vertex, directrix & vertex, focus & latus rectum.   P751#1,7,13,17,21,25,27,33,37,39
9.2          Celestial orbits of moons and planets are ellipses.
1. Given one specification of an ellipse, determine any of the others: equation, graph, foci & vertices, major & minor axes, eccentricity & foci.   P759#1,3,5,7,19,21,29,31,33,39,47
9.3          Some telescopes and some navigation systems use hyperbolas.
1. Given one specification of a hyperbola, determine any of the others: equation, graph, foci & vertices, major & minor axes, eccentricity & foci.   P768#1,3,5,11,17,19,27,31
9.4           Conic sections give us our last chance to use transformations (RST) on equations.
1. Use transformations (RST) on conics.   P781#1,19,21