Can someone please explain how I got this wrong?

Question

Write 5 R - 7 U in polar form.

Left = -Right

Down = - Up

(A) 8.60 ∠ 54.46°

(B) 8.60 ∠ 125.54°

(C) 8.60 ∠ 216.54°

(D) 8.60 ∠ 305.54°

(E) None of these

For this I got; (A) 8.60 ∠ 54.46°. However, the answer is incorrect. Can someone please explain how I got this question wrong?

Answer 1

Hello Jesset!

Note that the angle must have a negative sine (because of the -7U part), so cannot be 54.46°.

If we apply the Pythagoras theorem, we have:

c² = 7² + 5²

c² = 49 +25 = 74

sinθ = -√(49/74) = -54.46°

-54.46° = 360° - 54.46° = 305.54°

Letter D

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