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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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Comparing the two ratios 2/4 and 1/2<br> 2/4 is larger
kumpel [21]

Answer:

<em><u>3.5 : 7 > 1.2 : 2.5.</u></em>

Step-by-step explanation:

1. Compare the ratios 4 : 5 and 2 : 3.

Solution:

Express the given ratios as fraction

4 : 5 = 4/5 and 2 : 3 =2/3

Now find the L.C.M (least common multiple) of 5 and 3

The L.C.M (least common multiple) of 5 and 3 is 15.

Making the denominator of each fraction equal to 15, we have

4/5 = (4 ×3)/(5 ×3) = 12/15 and 2/3 = (2 ×5)/(3 ×5) = 10/15

Clearly, 12 > 10

Now, 12/15 > 10/15

Therefore, 4 : 5 > 2 : 3.

2. Compare the ratios 5 : 6 and 7 : 9.

Solution:

Express the given ratios as fraction

5 : 6 = 5/6 and 7 : 9 =7/9

Now find the L.C.M (least common multiple) of 6 and 9

The L.C.M (least common multiple) of 6 and 9 is 18.

Making the denominator of each fraction equal to 18, we have

5/6 = (5 ×3)/(6 ×3) = 15/18 and 7/9 = (7 ×2)/(9 ×2) = 14/18

Clearly, 15 > 14

Now, 15/18 > 14/18

Therefore, 5 : 6 > 7 : 9.

3. Compare the ratios 1.2 : 2.5 and 3.5 : 7.

Solution:

1.2 : 2.5 = 1.2/2.5 and 3.5 : 7 =3.5/7

1.2/2.5 = (1.2 ×10)/(2.5 ×10 ) = 12/25 and 3.5/7 = (3.5 ×10)/(7 ×10) = 35/70 = 1/2

[We removed the decimal point from the ratios now, we will compare the ratio]

Now find the L.C.M (least common multiple) of 25 and 2

The L.C.M (least common multiple) of 25 and 2 is 50.

Making the denominator of each fraction equal to 50, we have

= 12/25 = (12 ×2)/(25 ×2) = 24/50 and 1/2 = (1 ×25)/(2 ×25) = 25/50

Now, 25/50 > 24/50

Therefore, 3.5 : 7 > 1.2 : 2.5.

4 0
2 years ago
Find the value of x<br>​
riadik2000 [5.3K]

Answer:

need more information

Step-by-step explanation:

more information is needed to answer this question

3 0
3 years ago
Match the following items by evaluating the expression for x = -7. x-2 x-1 x0 x1 x2
frosja888 [35]

Answer:

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7 0
2 years ago
PLEASE HELP!!!
IrinaVladis [17]
44.


The closer it gets to -19, the closer the number goes to 44. It never hits it exactly though, but based off the trend (43.95, 43.995, 43.9995) we can tell that it gets closer to 44 each time.


Hope this helps! (:
8 0
2 years ago
If u add 5 to me and then divide by 9,u get 3. What number amI?
STatiana [176]
You are 22. If you add 22+5 you get 27. And if you divide 27 by 9 you get 3. So it is 22
6 0
3 years ago
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