Question

Which angle between –180° and 0 has the same cosine value as 275°

Answer 1

Answer:

cos (-85°)

Step-by-step explanation:

$\cos(275 \degree)$

since cosine is in fourth quadrant:

$\cos(275 \degree) = \cos( \{360 \degree - 275 \degree \}) \\ = \cos( - 85 \degree)$

Answer 2

-85° is the angle between –180° and 0° that has the same cosine value as 275°.

What is cosine?

Cosine is the trigonometric function that is equal to the ratio of the side adjacent to the acute angle in a right angled triangle.

Mathematically,

            Cos = Base/Hypotenuse

Now, to calculate cos(275) we have to first determine the quadrant of the given angle.

Since our angle is greater than 270 and less than or equal to 360, it is located in the Quadrant IV.

In the Quadrant IV, the values of cos are always positive.

275 is an obtuse angle so we can write,

Cos(275) = Cos{360+(-85)}

∵ Cos(360+θ) = Cosθ

∴ Cos{360+(-85)} = Cos(-85)

⇒ Cos(275) = Cos(-85)

The required answer is cos(275) = cos(-85)

Hence, -85° is the angle between –180° and 0° that has the same cosine value as 275°.

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