# Thread: QUEATION IN POLAR I am amazed by these solutions

1. ## QUEATION IN POLAR I am amazed by these solutions

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QUEATION IN POLAR I am amazed by these solutions

we now Q in one or third or fourth guadrant are diffrence

but here in this 2 quetion the solving are differnt when find Q Although the point in fourth guadrant in both quetion

See solving one why say - pi - 60
and anthoer 2 p- - 45

Although the point in fourth guadrant ??

see these soitions

2. Whenever cosθ is positive and sinθ is negative, θ is always in the fourth quadrant.

3. By the way, when you write " $2\pi- 60$" and " $2\pi- 45$ you are mixing "radians" and "degrees". Never do that!

In fact, except in problems specifically involving angles measured in degrees, you should always use radians.

Your answers should be $\sqrt{2}e^{(2\pi- \pi/4)i}= \sqrt{2}e^{7i\pi/4}$ and $2e^{(2\pi- 2\pi/3)i}= 2e^{4i\pi/3}$.

Of course, since $e^x$ has period $2i\pi$, you could more easily just write $\sqrt{2}e^{-i\pi/4}$ and $2e^{-2i\pi/3}$.

4. thanks but my question now why the answer in one - pi - 60
and anthoer 2 p- - 45 the point in foruth guadrant an As we know Angle in foruth guadrant = - pi - Q
why they use 2pi - Q ??????? this id my question

5. Originally Posted by r-soy
thanks but my question now why the answer in one - pi - 60
and anthoer 2 p- - 45 the point in foruth guadrant an As we know Angle in foruth guadrant = - pi - Q
why they use 2pi - Q ??????? this id my question
In the polar co-ordinates, the angle of rotation of the radius vector is measured in counter clockwise direction.
So the angle in the fourth quadrants is (2π - θ) or (3π/2 + θ)