Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal plac
es where appropriate. If there is no solution, enter NO SOLUTION.) 5 sin(2θ) − 2 sin(θ) = 0
1 answer:
Answer:
x = {kπ, arccos(1/5) +2kπ, 2kπ -arccos(1/5)}
Step-by-step explanation:
The double-angle trig identity for sine is useful:
5(2sin(θ)cos(θ)) -2sin(θ) = 0
2sin(θ)(5cos(θ) -1) = 0
This has solutions that make the factors zero:
θ = arcsin(0) = kπ
and ...
cos(θ) = 1/5
θ = arccos(1/5) +2kπ . . . . or . . . . 2kπ -arccos(1/5)
_____
Some numerical values are shown on the graph attached. values for multiples of pi are ...
{..., -12.566, -9.425, -6.283, -3.142, 0, 3.142, 6.283, 9.425, 12.566, ...}
You might be interested in
Check the picture below.
based on the equation, if we set y = 0, we'd end up with 0 = 0.5(x-3)(x-k).
and that will give us two x-intercepts, at x = 3 and x = k.
since the triangle is made by the x-intercepts and y-intercepts, then the parabola most likely has another x-intercept on the negative side of the x-axis, as you see in the picture, so chances are "k" is a negative value.
now, notice the picture, those intercepts make a triangle with a base = 3 + k, and height = y, where "y" is on the negative side.
let's find the y-intercept by setting x = 0 now,
now, we can plug those values on A = (1/2)bh,
Answer: Option 'd' is correct.
Step-by-step explanation:
Since we have given that
Number of hours of pop music = 3
Number of hours of classical music = 2
According to question, Every month onwards, the hours of pop music in her collection is 5% more than what she had the previous month. Her classical music does not change.
Rate of increment = 5% = 0.05
Let the number of months be 'x'.
So, our required function becomes,
Hence, Option 'd' is correct.