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nydimaria [60]
3 years ago
11

The exact value of cos5pi/12 is:​

Mathematics
1 answer:
jonny [76]3 years ago
4 0

Step 1: Convert \frac{5\pi }{12}, which is in radians into degrees. To convert it multiply by \frac{180}{\pi }

\frac{5\pi }{12} =\frac{180}{\pi }

900/12

75

Step 2: 75 degrees isn't on the unit circle but 45 degrees and 30 degrees is. Since 45 + 30 = 75 you can use the cosine of 45 and 30 to find the exact value

cos45 = \frac{\sqrt{2} }{2}

cos30 =\frac{\sqrt{3} }{2}

Step 3: Add the cos45 and cos30 to get cos5pi/12

\frac{\sqrt{2} }{2} +\frac{\sqrt{3} }{2} = \frac{\sqrt{2}+\sqrt{3}}{2}

Hope this helped!

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Suppose a circle has a radius of 13 inches. How far would a 24 inch chord be from the center of the circle? (Hint: Draw a diagra
lys-0071 [83]

Answer:

Step-by-step explanation:

Directions

  • Draw a circle
  • Dear a chord with a length of 24 inside the circle. You just have to label it as 24
  • Draw a radius that is perpendicular and a bisector through the chord
  • Draw a radius that is from the center of the circle to one end of the chord.
  • Label where the perpendicular radius to the chord intersect. Call it E.
  • You should get something that looks like  the diagram below. The only thing you have to do is put in the point E which is the midpoint of CB.

Givens

AC = 13 inches                   Given

CB = 24 inches                  Given

CE = 12 inches                    Construction and property of a midpoint.

So what we have now is a right triangle (ACE) with the right angle at E.

What we seek is AE

Formula

AC^2 = CE^2 + AE^2

13^2 = 12^2 + AE^2

169 = 144 + AE^2                     Subtract 144 from both sides.

169 - 144 = 144-144 + AE^2     Combine

25 = AE^2                                Take the square root of both sides

√25 = √AE^2

5 = AE

Answer

The 24 inch chord is 5 inches from the center of the circle.

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2 years ago
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Answer:

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Step-by-step explanation:

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Use the graph of f(x) = log x to obtain the graph of g(x) = log x + 5.
galina1969 [7]

The graph of g(x) = f(x) + 5 will have the graph of f(x) moved 5 units upward. The best choice is the last one.

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Adding 5 to each y-value (the output of f(x)) moves it upward by 5 units.

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A rectangle has a perimeter of 116 centimeters and a length of 26 centimeters. What is the width of the rectangle?
Andre45 [30]
26+26=52 which is the side lengths.
116-52=64 which is the other side lengths together. So one side length 32. 32+32+26+26=116
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4 years ago
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Two cargo ships spot a signal fire on a small island. The captains know they are 140 feet
Irina18 [472]

The distance from Ship B to the signal fire at point C is 405.4 \mathrm{ft}

Explanation:

It is given that two ships A and B are at a distance 140 ft from each other.

The angle formed by ship A is 82º and the angle formed by ship B is 78º.

To determine the distance from ship B to the signal fire at point C, we need to know the another angle.

Hence, we have,

\begin{aligned}\angle A+\angle B+\angle C &=180^{\circ} \\82^{\circ}+78^{\circ}+\angle C &=180^{\circ} \\160^{\circ}+\angle C &=180^{\circ} \\\angle C &=20^{\circ}\end{aligned}

Now, we shall solve the problem using the law of sines,

\frac{\sin A}{a}=\frac{\sin C}{c}

Substituting the values, we have,

\frac{\sin 82^{\circ}}{a}=\frac{\sin 20^{\circ}}{140}

\frac{0.9903}{a}=\frac{0.3420}{140}

Simplifying, we get,

a=\frac{0.9903 \times 140}{0.3420}

a=405.4

Thus, the distance from Ship B to the signal fire at point C is 405.4 \mathrm{ft}

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3 years ago
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