Question

Point P(5,0) is on the terminal arm of an angle k in standard position.

Answer 1

The value of the cosine of angle $k$ is 1.

Given a point $(x,y)$ that is a terminal arm of an angle $k$ in standard position, by trigonometric relations we have the following expression for the cosine:

$\cos k = \frac{x}{\sqrt{x^{2}+y^{2}}}$ (1)

Where:

• $k$ - Angle measure, in sexagesimal degrees.
• $x$ - Horizontal position of the point of the terminal arm, no unit.
• $y$ - Vertical position of the point of the terminal arm, no unit.

If we know that $x = 5$ and $y = 0$, then the cosine of the angle $k$ is:

$\cos k = \frac{5}{\sqrt{5^{2}+0^{2}}}$

$\cos k = 1$

The value of the cosine of angle $k$ is 1.

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