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3 years ago

A circle with a radius of 7 inches

Mathematics

2 answers:

Maslowich3 years ago

6 0

Diameter is 14 inches

zheka24 [161]3 years ago

6 0

The radius of this circle is 7 inches, so the diameter is 2(7) = 14 inches. The radius is half the diameter, or the diameter of this circle is 36 feet, so the radius is feet. The distance around a circle is called the circumference. So 14 inches.

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<u>Step-by-step explanation:</u>

Given: cos 330 = $\frac{\sqrt3}{2}$

Use the Double-Angle Identity: cos 2A = 2 cos² A - 1

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Proof LHS → RHS:

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Double-Angle: cos (2 · 165) = 2 cos² 165 - 1

⇒ cos 330 = 2 cos² 165 - 1

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$\rightarrow 2 \cos^2 165 = \dfrac{\sqrt3}{2} + \dfrac{2}{2}$

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Since cos 165 is in the 2nd Quadrant, the sign is NEGATIVE

$\rightarrow \cos 165 = - \dfrac{\sqrt3+1}{2\sqrt2}$

LHS = RHS $\checkmark$

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