What is the exact value of cos112.5?

The exact value of cos⁡ 112.5 is

Solution:

Use half angle formula for Cos,

(Since cos 112.5 is in II quadrant ,negative sign is used)            

cos⁡  225 = cos⁡ (45+180)

cos ⁡(a+b) = cos a cos b+sin a sin⁡ b

cos ⁡(45+180) = cos 45 cos⁡ 180+ sin⁡ 45 sin ⁡180

cos⁡ 180 = -1  

sin⁡ 180 = 0

apply equation 2 in equation 1

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!