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Salsk061 [2.6K]
3 years ago
13

Select all angle measures for which cos 0=1/2

Mathematics
2 answers:
Anna007 [38]3 years ago
5 0
The cosine ratio is the side adjacent over the hypotenuse in a right triangle.  If we set this reference angle up, the side adjacent to the reference angle has to be where x is positive because our 1/2 is a positive value.  The hypotenuse, no matter where it lies, is ALWAYS positive.  x is positive in the first and fourth quadrants.  Therefore, the value along the x axis is 1 and the hypotenuse is 2 (cosine is adjacent over hypotenuse...giving us our 1/2).  If the side adjacent is 1 and the hypotenuse is 2, the side across from the reference angle is the square root of 3, found using Pythagorean's theorem (or your knowledge of the Pythagorean triple for a 30-60-90 triangle).  The angle that lies across from the square root of 3 is the 60 degree angle in the first quadrant or a 300 degree angle in the fourth.  But we don't have the choice of a 60 or a 300!  We measure angles usually from the positive x axis counterclockwise.  This gives us the positive angle measure.  But if we measure the angle from the positive x axis clockwise, we measure the negative angle.  A positive 300 degree angle is the same thing as a -60 degree angle.  If the positive angle in the fourrth quadrant is a 300 degree angle and we go around the whole coordinate plane one more time (which is 360 degrees) we have 300+360 which is 660.  So your choices that are correct are -60° and 660°.  Now that we did them the correct way, by placing the angles in the coordinate plane, go ahead and check them on your calculator in degree mode to see that we are correct.
timurjin [86]3 years ago
5 0
The general solution to cos(theta) = 1/2 is 2k π ± π /3, translated to degrees, the solution is
360k ± 60 degrees, where k is an integer.

For k=0, we have solutions 0 ± 60, or  {-60, +60}
For k=1, we have solutions 360 ± 60, or  {300, 420}
For k=2, we have solutions 720 ± 60, or  {660, 780}

This is sufficient to cover the range of the answer choices, giving the angle measures for which cos(theta)=1/2 as {-60,660}
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3x + 12 = -6x - 9 and
Marianna [84]
  • Answer:

<em>1. x = - 7/3 = - 2  1/3</em>

<em>2. x = -2</em>

  • Step-by-step explanation:

<em>Hi there ! </em>

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<em>3x + 12 = - 6x - 9</em>

<em>3x + 6x = - 12 - 9</em>

<em>9x = - 21</em>

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<em>x = - 7/3</em>

<em>x = - 2  1/3</em>

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<em>12x + 20 = 2x</em>

<em>12x - 2x = - 20</em>

<em>10x = - 20</em>

<em>x = - 20/10</em>

<em>x = - 2</em>

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<em>Good luck !</em>

5 0
3 years ago
How many inches are in 14 feet, 8 inches? Enter only the number. Do not include units
blagie [28]

Answer:

176

Step-by-step explanation:

14x12 = 168 + 8 = 176

8 0
3 years ago
From a group of 11 people, 4 are randomly selected. What is the probability the 4 oldest people in the group were selected
asambeis [7]

Answer:

<h2>4/11</h2>

Step-by-step explanation:

Probability is the likelihood or chance that an event will occur.

<em>Probability = expected number of outcome/Total number of outcome</em>

If there are group of 11 people, then the total outcome of events will be 11

If we are to select 4 oldest people from the group, then the expected outcome is 4.

Hence, the probability that the 4 oldest people in the group were selected is 4/11.

3 0
4 years ago
Ruth has 7 more brown pencils than blue pencils, and 11 more blue pencils than red pencils. She has 5 red pencils. How many brow
olya-2409 [2.1K]

Answer: There are 5 red pencils, 16 blue pencils and 23 brown pencils.

Step-by-step explanation:

Since we have given that

Number of red pencils = 5

Number of blue pencils are 11 more than red pencils.

So, Number of blue pencils would be

11+5=16

Number of brown pencils are 7 more than blue pencils.

So, number of brown pencils would be

16+7=23

Hence, there are 5 red pencils, 16 blue pencils and 23 brown pencils.

8 0
3 years ago
A rectangle is 3 times as long as it is wide, and its perimeter is 80 centimeters. Find its dimensions
Free_Kalibri [48]

Say the width is W and the length is L

L=3W (and of course W=W)

Now you use the perimeter formula P=2L+2W

80=2(3W) + 2W)

80=6W+2W

80=8W Divide both sides by 8

W=10

Now that you know the width, substitute it back into L=3W to find the length

L=3(10)

L=30

The dimensions are length: 30 cm and width: 10 cm

8 0
4 years ago
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