How do you graph #theta=(5pi)/4#?

Answer 1

It is the line #y = x; x < 0#

This the 3rd quadrant, therefore, we must restrict x and y to be less than 0 , when we substitute #tan^-1(y/x)# for #theta#

#tan^-1(y/x) = (5pi)/4; x < 0 and y < 0#

Take the tangent of both sides:

#tan(tan^-1(y/x)) = tan((5pi)/4); x < 0 and y < 0#

The tangent "undoes" its inverse and substitute 1 for #tan((5pi)/4)#:

#y/x = 1; x < 0 and y < 0#

Multiply both sides by x:

#y = x; x < 0#

We dropped the restriction on y, because it is, now, a dependent variable.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email

Answer 2

Adam Aguirre

To graph the equation ( \theta = \frac{5\pi}{4} ), plot a point on the polar coordinate system located at an angle of ( \frac{5\pi}{4} ) radians from the positive x-axis. This point will be on the terminal side of the angle, and its distance from the origin will depend on the scale of the graph.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.