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Juliette [100K]
3 years ago
8

If sin = 5/12, find the exact values of cot and cos .

Mathematics
1 answer:
SashulF [63]3 years ago
7 0

The exact values of the cotangent and the cosine of the angle are \frac{\sqrt{119}}{5} and \frac{\sqrt{119}}{12}, respectively.

According to the information given, the angle resides in the <em>first</em> quadrant of the Cartesian plane. Hence, the cosine and the cotangent of the angle are also positive.

By trigonometry we remember the concepts of sine, cotangent and cosine:

\sin \theta = \frac{y}{r} (1)

\cos \theta = \frac{x}{r} (2)

\cot \theta = \frac{x}{y} (3)

Where r = \sqrt{x^{2}+y^{2}}.

If we know that y = 5 and r = 12, then the cotangent and the cosine of the angle are, respectively:

x = \sqrt{r^{2}-y^{2}}

x = \sqrt{12^{2}-5^{2}}

x = \sqrt{119}

\cos \theta = \frac{\sqrt{119}}{12}

\cot \theta = \frac{\sqrt{119}}{5}

The exact values of the cotangent and the cosine of the angle are \frac{\sqrt{119}}{5} and \frac{\sqrt{119}}{12}, respectively.

We kindly invite to check this question on trigonometric functions: brainly.com/question/6904750

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10 x 25 2/5 equals what
kramer

Answer:

254 is your answer

7 0
3 years ago
Can someone explain this I dont understand it
IrinaVladis [17]
Y = mx + b

m is your slope AKA rate of change
b is the y intercept.

from the graph we can see that the y intercept (b) is 15. (look at the y axis and see what point the line crosses on the y, here it is 15, in-between 10 and 20)

slope is rate of change. to figure this out remember slope = rise over run:

slope = \frac{rise}{run}

so pick two points. how much does one point rise after the other point you picked? In the graph it rises 1 square so rise = 1

Now looking at the same two points, how far away from each other are they on the x axis? Looking at the graph they are 2 squares away from each other. so run = 2

Now plug these numbers into the rise over run formula:

slope \: = \frac{1}{2}

Now we have everything we need to put into our formula for a line:

y = mx + b
y = \frac{1}{2} x + 18

For number 16 you should get:

y = \frac{1}{5} x + 3

after you do the same steps again yourself
8 0
3 years ago
HELP!!!!
ss7ja [257]
<h3>3 Answers: Choice D, Choice E, Choice F</h3>

============================================================

Explanation:

The inequality 6x - 10y ≥ 9 solves to y ≤ (3/5)x - 9/10 when you isolate y.

Graph the line y = (3/5)x - 9/10 and make this a solid line. The boundary line is solid due to the "or equal to" as part of the inequality sign. We shade below the boundary line because of the "less than" after we isolated for y.

Now graph all of the points given as I've done so in the diagram below. The points in the blue shaded region, or on the boundary line, are part of the solution set. Those points are D, E and F.

We can verify this algebraically. For instance, if we weren't sure point E was  a solution or not, we would plug the coordinates into the inequality to get...

6x - 10y ≥ 9

6(5) - 10(2) ≥ 9 .... plug in (x,y) = (5,2)

30 - 20 ≥ 9

10 ≥ 9 ... this is a true statement

Since we end up with a true statement, this verifies point E is one of the solutions. I'll let you check points D and F.

-----------

I'll show an example of something that doesn't work. Let's pick on point A.

We'll plug in (x,y) = (-1,1)

6x - 10y ≥ 9

6(-1) - 10(1) ≥ 9

-6 - 10 ≥ 9

-16 ≥ 9

The last inequality is false because -16 is smaller than 9. So this shows point A is not a solution. Choices B and C are non-solutions for similar reasons.

3 0
2 years ago
Berry waked the dog for 20 minutes.
Sergeu [11.5K]
Chris walked the dog for 80 minutes or 1 hour and 20 minutes
5 0
2 years ago
Read 2 more answers
How do you reduce 15/16
alina1380 [7]

Answer:

you can't because they don't have common factors

Step-by-step explanation:

8 0
3 years ago
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