Which of the following is a solution for the equation 1/485tan^2x = 0?
a) pi
b) pi/2
c) 485pi
d) no solution
Which of the following is NOT a solution to the equation 4sin^2x = 1 for 0≤x≤2pi?
a) 30 degrees
b) 210 degrees
c) 150 degrees
d) 120 degrees?
tan pi = 0
sin^2 x = 1/4
sin x = +/- 1/2
x = 30, 150 , 210, 330
To find the solution for the equation 1/485tan^2x = 0, we need to solve for x.
First, let's consider the given equation 1/485tan^2x = 0. In order for the equation to be equal to zero, the numerator 1 must be equal to zero, which is not possible. The equation 1/485tan^2x = 0 has no solution.
Therefore, the correct answer is (d) no solution.
Now, let's move on to the second question.
To find the solution for the equation 4sin^2x = 1, we need to solve for x within the range of 0 ≤ x ≤ 2pi.
First, let's rewrite the equation as sin^2x = 1/4.
Next, we take the square root of both sides of the equation, resulting in sinx = ±1/2.
Now we need to find the values of x that satisfy sinx = ±1/2 in the given range.
The values of x for sinx = 1/2 are 30 degrees and 150 degrees. However, since the given range is in radians, we need to convert these degrees to radians.
Converting 30 degrees to radians, we get π/6.
Converting 150 degrees to radians, we get 5π/6.
Therefore, the correct answer is (c) 150 degrees.
Similarly, the values of x for sinx = -1/2 are 210 degrees and 330 degrees. Converting these degrees to radians, we get 7π/6 and 11π/6, respectively.
Since all the answer options provided are in degrees, they need to be converted to radians as we did above.
Therefore, the correct answer is (a) 30 degrees.
In summary:
- For the equation 1/485tan^2x = 0, the answer is (d) no solution.
- For the equation 4sin^2x = 1, the correct answer is (a) 30 degrees.