Answer:
There are no numbers/pictures.
Step-by-step explanation:
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:
answer a
Step-by-step explanation:
< 
- Let's isolate
on one side of the equation. Ignore the inequality for now. We'll deal with that later.
- Now, I'm going to bring back the inequality or < symbol. I only removed it when simplifying and isolating , but if this confuses you, just do your math and keep the inequality there.
< 
- On a number line, this would include every number <em>less than </em>, due to the < (less than) symbol. This disqualifies answers b and d because they are showing every number <em>greater than </em>. But, how do we decide between answers a and c?
- If a line has point at its beginning, , then that means that every number <em>less than or equal to</em> [ ≤ ] 6 is being shown, but our equation just says <em>less than </em>[ < ] 6, so answer a is our correct answer.
