Answer:
n = π/6, π/4, 3π/4, 5π/6
Step-by-step explanation:
sin(3n) − sin n = cos(2n)
Use double and triple angle formulas:
(3 sin n − 4 sin³ n) − sin n = 1 − 2 sin² n
2 sin n − 4 sin³ n = 1 − 2 sin² n
4 sin³ n − 2 sin² n − 2 sin n + 1 = 0
Factor by grouping:
2 sin² n (2 sin n − 1) − (2 sin n − 1) = 0
(2 sin² n − 1) (2 sin n − 1) = 0
Solve:
2 sin² n − 1 = 0
2 sin² n = 1
sin² n = 1/2
sin n = √2/2
n = π/4, 3π/4
2 sin n − 1 = 0
2 sin n = 1
sin n = 1/2
n = π/6, 5π/6
Answer:
1. x>20 2. x≤1 3.x<4 4.x>9 5.x≥-13
Hey there!
Tim drives 300 kilometers.
Work: 80 x 3 = 240
Then, 45 minutes is 3/4 of an hour, so if you were to do 3/4 of 80 it is 60
Now, add 240 + 60 = 300
Hope I was able to help!
7). C
8). 60
n = 5(10) + 10
n = 50 + 10
n = 60
9). 17
f(x) = -2x + 7 plug the -5 in for x
f(x) = -2(-5) + 7
= 10 + 7
= 17
10).
