For an angle θ with the point (12, -5) on its terminating side, what is the value of cosine?

Solution:

The above problem can be represented pictorially by the diagram given below:

The point on the circumference of the circle represented as (12, -5) implies that x = 12 and y = -5.

The angle θ subtends the arc AB on the circumference. By dropping a perpendicular line from point B onto OA, we get a right-angled triangle ∠OAB. As the coordinates of point B are (12,-5) it implies:

A'B = 5 and OA' = 12.

The hypotenuse OB can be obtained by applying the pythagorean theorem by using the relationship:

OB² = OA'² + A'B²

OB² = (12)² + (5)²

OB² = 144 + 25 = 169

OB = √169

OB = 13

Now Cosine of the angle θ is defined as :

Cosθ = adjacent side/hypotenuse

OA'/OB = 12/13

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For an angle θ with the point (12, -5) on its terminating side, what is the value of cosine?

Summary:

For an angle θ with the point (12, -5) on its terminating side, the value of cosine is 12/13.