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Factor the trigonometric expression completely. 3 csc2 Y + 7 csc Y+2

Factor the trigonometric expression completely. 3 csc2 Y + 7 csc Y+2

Trigonometry (11th Edition)
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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Kindly explain why "cscY" remains in parenthesis after factoring out 3cscY. Wouldn't factoring it back in produce 3csc2Y2?

Factor the trigonometric expression completely. 3 csc2 Y + 7 csc Y+2 This expression is in the form ax + bx + c, where x = csc Y, a = 3, b= 7, and c= 2. Using the ac-method for factoring, you must find two numbers whose product is a•c and whose sum is b. In this case, a•c= 6 and b = 7. The two numbers with this property are 6 and 1. Next, rewrite the expression by replacing 7 with the sum of these two numbers. 3 csc? Y + 7 csc Y +2= 3 csc2 Y + 6 csc Y + 1 csc Y +2 Factor the resulting four-term polynomial by grouping: 3 csc2 Y + 6 csc Y+ 1 csc Y+2 = 3 csc Y(csc Y + 2) + 1 ( csc Y + 2) CsC = (csc Y + 2)(3 csc Y + 1)
Transcribed Image Text:Factor the trigonometric expression completely. 3 csc2 Y + 7 csc Y+2 This expression is in the form ax + bx + c, where x = csc Y, a = 3, b= 7, and c= 2. Using the ac-method for factoring, you must find two numbers whose product is a•c and whose sum is b. In this case, a•c= 6 and b = 7. The two numbers with this property are 6 and 1. Next, rewrite the expression by replacing 7 with the sum of these two numbers. 3 csc? Y + 7 csc Y +2= 3 csc2 Y + 6 csc Y + 1 csc Y +2 Factor the resulting four-term polynomial by grouping: 3 csc2 Y + 6 csc Y+ 1 csc Y+2 = 3 csc Y(csc Y + 2) + 1 ( csc Y + 2) CsC = (csc Y + 2)(3 csc Y + 1)
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