SOLUTION: 1. Find the exact value of the following given that sec𝛼 =5 and 270°<𝛼<360°. sin𝛼/2 2. Express the product as a sum then find the sum’s exact value. cos1

Algebra ->  Trigonometry-basics -> SOLUTION: 1. Find the exact value of the following given that sec𝛼 =5 and 270°<𝛼<360°. sin𝛼/2 2. Express the product as a sum then find the sum’s exact value. cos1      Log On


   

Question 1187014: 1. Find the exact value of the following given that sec𝛼 =5 and 270°<𝛼<360°.

sin𝛼/2
2. Express the product as a sum then find the sum’s exact value.

cos11𝜋/12cos𝜋/12
Hello! For these two problems, I am very confused about what to do. I need help solving both from the beginning.
Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
1. Find the exact value of the following given that sec𝛼 =5 and 270°<𝛼<360°.

sin𝛼/2
===================
sec(A) = 5 ---> cos(A) = 1/5
sin(A) = sqrt(1 - cos^2) = sqrt(24/25) = 2sqrt(6)/5
-----
Look up Half Angle Formulas on Wikipedia for sin(A/2)

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Use parentheses!!!

1. Is it sin(a/2) = sin%28a%2F2%29? Or is it (sin(a))/2 = %28sin%28a%29%29%2F2

2. This one, "cos11𝜋/12cos𝜋/12" can be interpreted many different ways. Since you say it is a product, you probably mean (cos(11pi/12))*(cos(pi/12)) = %28cos%2811pi%2F12%29%29%2A%28cos%28pi%2F12%29%29

But we tutors should not need to guess what it is that you write in your posts....

Re-post, showing the problems clearly.

NOTE!!! One problem per post, so post them separately.