Question

Choose the point on the terminal side of -45°.

(-3, -3)
(4, -4)
(5, 5)
(-2, 2)

Answer 1

Answer on Question #57376 – Math – Analytic Geometry

Question

Choose the point on the terminal side of $-45{}^{\circ}$.

(-3, -3)

(4, -4)

(5, 5)

(-2, 2)

Solution

If a point is on the terminal side of $-45^o$ then this means that

$$x = t \cdot \cos(-45^o), \quad y = t \cdot \sin(-45^o), \quad t > 0;$$ $$\cos(-45^o) = \frac{\sqrt{2}}{2} > 0, \quad \sin(-45^o) = -\frac{\sqrt{2}}{2} < 0;$$

$x > 0, y < 0$; Only point $(x, y) = (4, -4)$ has $x > 0$ and $y < 0$.

Answer: (4; -4).

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