SOLUTION: How can i transform {{{ 3cis(-5pi/6) }}} in to Cartesian form? (or known as rectangular form)
The problem I'm having is, How can i find the Radian Value of {{{ cos(-5pi/6)}}} an
Question 1029365: How can i transform in to Cartesian form? (or known as rectangular form)
The problem I'm having is, How can i find the Radian Value of and . Which is used to turn this polar form in to Cartesian form?
without Calculator!!
Thanks!!!! Found 2 solutions by Alan3354, Edwin McCravy:Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! How can i transform in to Cartesian form? (or known as rectangular form)
The problem I'm having is, How can i find the Radian Value of and . Which is used to turn this polar form in to Cartesian form?
without Calculator!!
==================
cos(-5pi/6) = cos(5pi/6) = -sqrt(3)/2
sin(-5pi/6) = -sin(5pi/6) = -1/2
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3cis(-5pi/6) = -3sqrt(3)/2 - 3i/2
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You can't do a Master's thesis on this.
If you're dealing with "cis" and conversions to Cartesian form, you have to know how to do this.
The other tutor just blurted out the answers.
Here is how we learn to come up with them:
Change to degrees:
Add 360°: -150°+360° = 210°
That's in QIII, so we draw the angle:
The reference angle is the acute angle between the
radius vector and the x-axis. So for 210°, the
reference angle is gotten by subtracting 180°
from it, getting 210°-180° = 30°
Then we learn the 5 special angles, by memorizing this chart:
If we want sine we read from the left across with the angles
at the top, and if we want cosine we read from the right across
using the angles at the bottom:
Then we memorize:
"All Students Take Calculus", which is a mnemonic device
that is used to help students memorize the sign values
of all the trigonometric functions in the 2-dimensional
Cartesian coordinate system. The letters ASTC signify
which of the trigonometric functions are positive,
in the order of the quadrants - starting in the top
right quadrant, and moving counterclockwise.
In Quadrant I: A for All - all trigonometric functions
are positive in this quadrant.
In Quadrant II: S for Sine - sine and cosecant functions
are positive in this quadrant.
In Quadrant III: T for Tangent - tangent and cotangent
functions are positive in this quadrant.
In Quadrant IV: C for Cosine - cosine and secant functions
are positive in this quadrant.
So therefore both the cosine and sine are negative in
quadrant QIII.
and
Edwin
