Learning guidelines **Educational Resource: Trigonometric Identities and Expressions**1. **Express the Product as a Sum or Difference:** Express the given product as a sum or difference containing only sines or cosines: \[ \sin(5x)\cos(3x) = \_\_\_\_ \]2. **Expression Using Sine, Cosine, or Tangent of a Single Angle:** Write the expression using the sine, cosine, or tangent of a single angle. Then find the exact value of the expression: \[ \frac{\tan 35^\circ + \tan 10^\circ}{1 - \tan 35^\circ \tan 10^\circ} \] Write it as: \[ \tan(35^\circ + 10^\circ) = \_\_\_\_ \] Find the exact value: \[ \frac{\tan 35^\circ + \tan 10^\circ}{1 - \tan 35^\circ \tan 10^\circ} = \_\_\_\_ \]3. **Verify the Identity:** Verify the given identity: \[ \frac{\cos x - \cos y}{\cos x + \cos y} = -\tan \left( \frac{x+y}{2} \right) \tan \left( \frac{x-y}{2} \right) \] Steps to verify: a. Start with the numerator of the left side and apply the appropriate formula of sum to product. b. Use the sum to product formula on the denominator of the left side: \[ \cos x + \cos y = \_\_\_\_ \] c. In the numerator and denominator, substitute the expressions found in previous steps. Then divide out the common factor of the expression: \[ \_\_\_\_ \] d. The fraction from the previous step then simplifies to: \[ \tan \left( \frac{x+y}{2} \right) \tan \left( \frac{x-y}{2} \right) \] Using what identity? - Reciprocal - Quotient - Pythagorean (strikethrough indicates this is incorrect) - Even-Odd Check 1Remember, when

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Expros on ly the given product Sum or differance containing as sines Cosines. or sin (s-) cos (sn) = 2. Write the expression as find the sine, cosine ,or of tangent. value of the exprossion an angle. Then the exaot tan 35° + tan 10° 1-tan 35° tan 10" Write the expression. the tangent of a sine, cosine, or single as angle. tan 35°+tan 10° 1-tan 35° tan 10° Find the exact value of the expression. tan 35°+ tan 10° 1-tan 35° tan 10° 3.) Verity the identity. Cos x- Cos y:tan + cos y with the tan X-y Cos 2 numerator of the left side to product. Start and apply the appropriate formula ot x- cos 9 Sum a. cos sum to product formula on the denominator of Now use the the left side. X + cos y b.cos denominator, substitute divide. expressions factor and the c)In the found of the nume rator out the common in pre vious steps. Then. expre ssion. d) The fraction from the previous step then simplifies to using what ? O Quotient Identity X+4 tan 2 tan O Reciprical Identity O Pythagorean a Identity O Even - Odd Identity

Expros on ly the given product Sum or differance containing as sines Cosines. or sin (s-) cos (sn) = 2. Write the expression as find the sine, cosine ,or of tangent. value of the exprossion an angle. Then the exaot tan 35° + tan 10° 1-tan 35° tan 10" Write the expression. the tangent of a sine, cosine, or single as angle. tan 35°+tan 10° 1-tan 35° tan 10° Find the exact value of the expression. tan 35°+ tan 10° 1-tan 35° tan 10° 3.) Verity the identity. Cos x- Cos y:tan + cos y with the tan X-y Cos 2 numerator of the left side to product. Start and apply the appropriate formula ot x- cos 9 Sum a. cos sum to product formula on the denominator of Now use the the left side. X + cos y b.cos denominator, substitute divide. expressions factor and the c)In the found of the nume rator out the common in pre vious steps. Then. expre ssion. d) The fraction from the previous step then simplifies to using what ? O Quotient Identity X+4 tan 2 tan O Reciprical Identity O Pythagorean a Identity O Even - Odd Identity

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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