Help I need this rn! And please explain

Mathematics

1 answer:

slamgirl [31]1 year ago

4 0

Answer:

(4, 0)

Step-by-step explanation:

The circumference of a circle is $2 \pi r$ where <em>r</em> is the radius.

In this case, $2 \pi r = 10 \pi$ . Divide both sides of the equation by $2\pi$ to get

$r=5$

The center of the circle is on the <em>x</em>-axis, so the intercepts are 5 units to the left of the center and 5 units to the right of the center. The two intercepts are (-1-5, 0) and (-1+5, 0). The point that is on the positive <em>x</em>-axis is (4, 0).

See attached image.

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How do I get this answer?

Keith_Richards [23]

Answer:

Step-by-step explanation:

Several trig identities are involved in the proof of this. This is the order in which they are used.

cos(2x) = cos²(x) -sin²(x)
cos²(x) +sin²(x) = 1
cos(x) = 1/sec(x)

<h3>Proof</h3>

Starting with the left side, we can transform it into the right side.

$2\cos(2x)=2(\cos^2(x)-\sin^2(x)) = 2(\cos^2(x)-(1-\cos^2(x)))\\\\=2(2\cos^2(x)-1)=2\left(\dfrac{2}{\sec^2(x)}-\dfrac{\sec^2(x)}{\sec^2(x)}\right)\\\\=\boxed{\dfrac{4-2\sec^2(x)}{\sec^2(x)}}$