Determine sinx tanx-sinx=0 for 0≤ x < 360°.
To determine the solution for the equation sin(x) tan(x) - sin(x) = 0, we can first factor out the common term:
sin(x)(tan(x) - 1) = 0
Now, we can set each factor equal to zero and solve for x.
First, consider sin(x) = 0. In the range 0 ≤ x < 360°, sin(x) will be equal to zero when x is a multiple of 180°:
x = 180°k, where k is an integer.
Next, consider tan(x) - 1 = 0. To solve this equation, we need to find the values of x where tan(x) equals 1. The tangent function is equal to 1 at two angles in the range 0 ≤ x < 360°: 45° and 225°.
Thus, we have two possible solutions for x:
1. x = 45°
2. x = 225°
Therefore, the solution to the equation sin(x) tan(x) - sin(x) = 0 for 0 ≤ x < 360° is x = 45° and x = 225°.
To determine the values of x for which sin(x) tan(x) - sin(x) = 0, we can factor out the common term sin(x):
sin(x) (tan(x) - 1) = 0
Now, we have two cases to consider:
1. sin(x) = 0
2. tan(x) - 1 = 0
Case 1: sin(x) = 0
When sin(x) = 0, x can take the values of 0°, 180°, and 360°.
Case 2: tan(x) - 1 = 0
To solve for x in this case, we need to find the values of x for which tan(x) = 1.
For 0 ≤ x < 360°, tan(x) = 1 at x = 45° and x = 225°.
Therefore, the values of x for which sin(x) tan(x) - sin(x) = 0, for 0≤ x < 360°, are:
x = 0°, 45°, 180°, 225°, and 360°.