Answer:
(364.0, 236.4)
Explanation:
You want the vector 434∠33° written as an ordered pair.
Ordered pair
The "ordered pair" representation of a vector can take different forms. we're not sure the form your curriculum materials are asking for, so we'll show it a couple of ways.
(magnitude; direction) = (434; 33°) or maybe (434, 33)
(x, y) = 434·(cos(33°), sin(33°) ≈ (364.0, 236.4)
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Additional comment
We like the form used in the problem statement above (434∠33°) for vectors expressed in polar form. For vectors expressed in rectangular form, many calculators work nicely with a complex number representation (364 +236.4i).
The ordered pair using a semicolon (;) separator is written that way to distinguish it from the (x, y) ordered pair. That form is used by some geometry software. A calculator may use [434, 33] or [364, 236.4] (for example), leaving it up to the user to remember what the pair represents.
Some authors use a combination of complex and polar representations like this:
A(cos(B) +i·sin(B)) = A·cis(B)
In this, the "cis" is a reminder of the "cosine + i·sine" complex number representation. It is also a longer way to write A∠B.
The second attachment shows our preferred calculator using our preferred vector notations. YMMV
→ Be sure your calculator is in "degrees" mode.