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11 a b 12 a b evaluate exactly using sum and

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11. a.b.12. a.b.Evaluate exactly using sum and difference formulas.13. a.b.Rewrite as a single expression using sum and difference formulas.14. a.b.Evaluate exactly using sum and difference formulas, by reducing the angle to an angle inor15. a.b.Use a cofunction identity to write an equivalent expression for the one given.16. a.b.17.Verify that both expressions yield the same result using sum and difference formulas:and.18.Use sum and difference formulas to verify the following identity.SECTION 7.4The Double-Angle, Half-Angle, and Pr oduct-to-Sum IdentitiesKEY CONCEPTSWhen multiple angle identities (identities involving) are used to find exact values, the terminal side ofmustbe determined so the appropriate sign can be used.The power reduction identities for cos2xand sin2xare closely related to the double-angle identities, and can bederived directly fromand.The half-angle identities can be developed from the power reduction identities by using a change of variable andtaking square roots. The sign is then chosen based on the quadrant of the half angle.The product-to-sum and sum-to-product identities can be derived using the sum and difference formulas, and haveimportant applications in many areas of science.cos12x212 sin2xcos12x22 cos2x1ncosax6bcosax6b13cosxtan 15°tan1135°120°2tan 15°tan145°30°2sinax12bcosax8bsina574bcos 1170°30, 22.30, 360°2sinax4bcosa3x8bcosax4bsina3x8bcos13x2cos12x2sin13x2sin12x2sin 139° cos 19°cos 139° sin 19°cos 109° cos 71°sin 109° sin 71°sina12btan 15°tana12bcos 75°sin12sincoscossinsin12cos12coscossinsincos12cos cossin sincos1230°, 360°2cob19537_ch07_733-742.qxd1/26/114:07 PMPage 734
7–83Summary and Concept Review735Precalculus—EXERCISESFind exact values for, andusing the information given.19. a.in QIVb.in QIIIFind exact values for, andusing the information given.20. a.in QIIb.in QIIFind exact values using the appropriate double-angle identity.21. a.b.Find exact values forandusing the appropriate half-angle identity.22. a.b.Find exact values forandusing the given information.23. a.in QIVb.in QIV24.Verify the equation is an identity.25.Solve using a sum-to-product formula.26.The area of an isosceles triangle (two equal sides) is given by the formulawhere the equalsides have lengthxand the vertex angle measures(a) Use this formula and the half-angle identities to find thearea of an isosceles triangle with vertex angleand equal sides of 12 cm. (b) Use substitution and adouble-angle identity to verify thatthen recompute the triangle’s area. Do theresults match?SECTION 7.5The Inverse T rig Functions and Their ApplicationsKEY CONCEPTSIn order to create one-to-one functions, the domains of, andare restricted as follows:(a); (b); and (c).Forthe inverse function is given implicitly asand explicitly asorThe expressionis read, “yis the angle or real number whose sine isx.” The other inverse functions aresimilarly read/understood.

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Term
Winter
Professor
NoProfessor
Tags
Trigonometry, Inverses, Families of Identities

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