There are a couple of different approaches you can use for this. Here's one.
1. Determine how many digits repeat. (There is just one repeating digit.)
2. Call your number x. Multiply x by 10 to the power of the number of digits found in step 1.
3. Subtract the original number, then solve for x.
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If you recognize that 0.333... (repeating) is 1/3, then you know that 0.0333... (repeating) is 1/10×1/3 = 1/30. Add that to 0.8 = 4/5 and you get
... 4/5 + 1/30 = 24/30 + 1/30 = 25/30 = 5/6
Answer:
For a point defined bt a radius R, and an angle θ measured from the positive x-axis (like the one in the image)
The transformation to rectangular coordinates is written as:
x = R*cos(θ)
y = R*sin(θ)
Here we are in the unit circle, so we have a radius equal to 1, so R = 1.
Then the exact coordinates of the point are:
(cos(θ), sin(θ))
2) We want to mark a point Q in the unit circle sch that the tangent has a value of 0.
Remember that:
tan(x) = sin(x)/cos(x)
So if sin(x) = 0, then:
tan(x) = sin(x)/cos(x) = 0/cos(x) = 0
So tan(x) is 0 in the points such that the sine function is zero.
These values are:
sin(0°) = 0
sin(180°) = 0
Then the two possible points where the tangent is zero are the ones drawn in the image below.
