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Juliette [100K]
2 years ago
8

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

Mathematics
1 answer:
SashulF [63]2 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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