Answer:
the portion of the x-axis that the straight line cuts is the interval [5r, -5r].
Explanation:
To find the portion of the x-axis that the straight line cuts, we first need to solve the equation for θ. The sine function has a range of [-1, 1], so the value of r must be greater than or equal to 5 in order for the equation to have a solution.
To solve the equation, we can use the fact that sin(π/4 - θ) = cos(θ). Therefore, the equation can be rewritten as:
cos(θ) = 5
We can then use the fact that cos(θ) = x/r to solve for x:
x = 5r
Therefore, the portion of the x-axis that the straight line cuts is the interval [5r, -5r].
Note that this is only valid if r is greater than or equal to 5. If r is less than 5, there are no solutions to the equation and the straight line does not cut the x-axis.