Answered

Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Connect with professionals ready to provide precise answers to your questions on our comprehensive Q&A platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

use a sum or difference identity to find an exact value of sin 2pi over 12

Sagot :

tron1368
5pi/12 = 3pi/12 + 2pi/12 = pi/4 + pi/6 

sin(a + b) => sin(a)cos(b) + sin(b)cos(a) 
cos(a + b) => cos(a)cos(b) - sin(a)sin(b) 

sin(5pi/12) => 
sin(3pi/12 + 2pi/12) => 
sin(pi/4 + pi/6) => 
sin(pi/4)cos(pi/6) + sin(pi/6)cos(pi/4) => 
(sqrt(2)/2) * (sqrt(3)/2) + (1/2) * (sqrt(2)/2) => 
(sqrt(2)/4) * (1 + sqrt(3)) 

cos(5pi/12) => 
cos(pi/4 + pi/6) => 
cos(pi/4)cos(pi/6) - sin(pi/4)sin(pi/6) => 
(sqrt(2)/2) * (sqrt(3)/2) - (sqrt(2)/2) * (1/2) => 
(sqrt(2)/4) * (sqrt(3) - 1) 

tan(5pi/12) => 
sin(5pi/12) / cos(5pi/12) => 
(sqrt(2)/4) * (sqrt(3) + 1) / ((sqrt(2)/4) * (sqrt(3) - 1)) => 
(sqrt(3) + 1) / (sqrt(3) - 1) => 
(sqrt(3) + 1)^2 / (3 - 1) => 
(3 + 2 * sqrt(3) + 1) / 2 => 
(4 + 2 * sqrt(3)) / 2 => 
2 + sqrt(3) 

csc(5pi/12) => 
1 / sin(5pi/12) => 
4 / (sqrt(2) * (sqrt(3) + 1)) => 
4 * sqrt(2) * (sqrt(3) - 1)) / (2 * (3 - 1)) => 
4 * sqrt(2) * (sqrt(3) - 1)) / (2 * 2) => 
sqrt(2) * (sqrt(3) - 1) 

sec(5pi/12) => 
1/cos(5pi/12) => 
4 / (sqrt(2) * (sqrt(3) - 1)) => 
4 * sqrt(2) * (sqrt(3) + 1)) / (2 * (3 - 1)) => 
sqrt(2) * (sqrt(3) + 1) 

cot(5pi/12) => 
1/tan(5pi/12) => 
1 / (2 + sqrt(3)) => 
(2 - sqrt(3)) / (4 - 3) => 
2 - sqrt(3)
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.