Determine all the possible values of x where 0 deg is more than or equal to x and x is more or equal to 360 deg such that
i'm not sure the solution, please correct it,
sin x sec x - 3 sin x = 0
the solution:
sin x 1/cos x - 3 sin x = 0
sin x - 3 sin x = cos x
then i don't know how to continue....
To solve the equation sin(x)sec(x) - 3sin(x) = 0, let's continue from where you left off.
sin(x) - 3sin(x) = cos(x)
Now, let's simplify the equation further. Combine like terms on the left side:
-2sin(x) = cos(x)
Since sin(x)/cos(x) is equivalent to tan(x), we can rewrite the equation as:
-2sin(x) = 1/tan(x)
Multiplying both sides by tan(x) gives:
-2sin(x)tan(x) = 1
Now, we know that the identity sin(x)tan(x) = 1 holds true when x is equal to the special angles kπ, where k is an integer. Therefore, we can write:
-2sin(x)tan(x) = -2tan(x)sin(x) = 1
Solving for x, we have two cases to consider:
Case 1: -2tan(x) = 1, which implies tan(x) = -1/2
Looking at the unit circle, we find that x = π/6 + kπ, or 30 degrees + k * 180 degrees, for k being an integer.
Case 2: sin(x) = 0
In this case, x can take on any value that makes sin(x) equal to 0. This occurs when x = kπ, or k * 180 degrees, where k is an integer.
Therefore, the possible values of x that satisfy the equation sin(x)sec(x) - 3sin(x) = 0 are:
x = π/6 + kπ (30 degrees + k * 180 degrees), and
x = kπ (k * 180 degrees), where k is an integer.