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3 years ago

Angle A is circumscribed about circle O. What is the measure of angle O? 46

Mathematics

1 answer:

masya89 [10]3 years ago

5 0

Answer:

m<O = 134°

Step-by-step explanation:

OC = OB = radius of the circle

AC = AB = tangents of circle O

m<C = m<B = 90°. (Tangent and a radius always form 90°)

m<A = 46°

Therefore,

m<O = 360° - (m<C + m sum of angles in a quadrilateral.

m<O = 360° - (90° + 90° + 46°)

m<O = 360° - 226°

m<O = 134°.

Measure of angle A = 134°

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Convert the Cartesian equation (x 2 + y 2)2 = 4(x 2 - y 2) to a polar equation.

SashulF [63]

ANSWER

${r}^{2} = 4 \cos2\theta$

EXPLANATION

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This implies that

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Let us evaluate the exponents to get:

${r}^{4} = 4({ {r}^{2} \cos^{2}\theta } - {r}^{2} \sin^{2}\theta)$

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Divide through by r²

${r}^{2} = 4 ({ \cos^{2}\theta } - \sin^{2}\theta)$

Apply the double angle identity

$\cos^{2}\theta -\sin^{2}\theta= \cos(2 \theta)$

The polar equation then becomes:

${r}^{2} = 4 \cos2\theta$

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