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# Class Note for MATH 1330 at UH

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This 5 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 16 views.

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Date Created: 02/06/15

Example 5 Factor the following expression sin26 csc2 6 Example 6 Factor the following expression 9 tan2 6 36 cot2 6 Example 7 Factor the following expression 0302 6 l 9 csc6 90 An identity is an equation that is true for all allowed values of its variable or variables Basic Trigonometric Identities Reciprocal Identities sin6 l l tan6 cos6 5 cot6 tan6 2 cot6 3 csc6 Sinlog 4 sec6 1 cos6 Pythagorean Identities l sin26 00526 1 2 tan2 6 l 2 sec2 6 3 0096 l cscz6 Example 8 Simplify the following secx cotx Example 9 Simplify the following 1 sin2 x cos2 x 1 Example 10 Simplify the following csc2 x tanx cotx Example 11 Simplify the following 1 sinxsecx tanx Example 12 Simplify the following cosx tanltxgt 1 sinx Example 13 If cos9 g and 270 lt 9 lt 3600 find the exact values of 5609 and sin6 12 7r Example 14 If 00t6 and E lt 6 lt 7239 find the exact values of each of the remaimng five trigonometric functions 0 g Verifying Identities To verify that an equation is a trigonometric identity we can show that one side of the equation can be transformed into the other side of the equation by using known identities andor performing indicated operations on the given expression on that side Helpful Hints on Proving Identities 1 Do not assume that the lefthand side is equal to the righthand side 2 Choose to simplify the most complicated side by using known identities 3 Convert all terms to sine and cosine This usually helps 4 Find common denominators 5 Simplify the chosen side of the equation to make it look like the other side of the equation Example 15 Prove the following identity tanx cotx secx cscx Example 16 Prove the following identity tanltxgt secx sinx Example 17 Prove the following identity sinx 1 cosx cotx cscx Example 18 Prove the following identity ZCSCOC sinx 1 cosx 1 cosx sinx Math 1330 Section 44 Trigonometric Expressions and Identities Operations on Trigonometric Expressions We simplify add subtract multiply divide and factor trigonometric expressions in the same manner as we simplify add subtract multiply divide and factor algebraic expressions Example 1 Perform the following operation and combine like terms tan64tan610 Example 2 Perform the following operation and combine like terms sec9 12 Example 3 Perform the following operation and combine like terms 1 l 8 cos6 sin6 Example 4 Perform the following operation and combine like terms 23 csc8 tan8 13 csc8 tan9

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