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Marat540 [252]
2 years ago
10

If tan 0= -(3)/(8), which expression is equivalent to cot 0 ?

Mathematics
2 answers:
IgorLugansk [536]2 years ago
8 0
Tan x = sin x / cos x

cot x = cos x/ sin x

We can see that tan and cot are reciprocal.

So, if tan(O)  = -(3)/(8), then cot(O) = - (8)/3.
DochEvi [55]2 years ago
8 0
<h2>Answer:</h2>

Hence, the answer is:

      \cot O=\dfrac{1}{\dfrac{-3}{8}} or  \cot 0=\dfrac{-8}{3}

<h2>Step-by-step explanation:</h2>

We know that the tangent trignometric function and the cotangent trignometric function is given by:

         \tan x=\dfrac{1}{\cot x}

i.e. the tangent function and the cotangent function are inverse of each other.

We are given tangent of an angle O as:

\tan 0=\dfrac{-3}{8}

Hence, we have:

\cot O=\dfrac{1}{\tan O}\\\\i.e.\\\\\cot O=\dfrac{1}{\dfrac{-3}{8}}\\\\i.e.\\\\\cot O=\dfrac{8}{-3}\\\\i.e.\\\\\cot 0=\dfrac{-8}{3}

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The given question is a quadratic equation and we can use several methods to get the solutions to this question. The solution to the equation are 3/4 and -5/6 and the greater of the two solutions is 3/4

<h3>Quadratic Equation</h3>

Quadratic equation are polynomials with a second degree as it's highest power.

An example of a quadratic equation is

y = ax^2 + bx + c

The given quadratic equation is 24x^2 + 2x = 15

Let's rearrange the equation

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The equation or formula of quadratic formula is given as

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We can substitute the values into the equation and solve

y = \frac{-b +- \sqrt{b^2 - 4ac} }{2a}\\y = \frac{-2 +- \sqrt{2^2 -4 * 24 * (-15)} }{2*24} \\y = \frac{-2+-\sqrt{4+1440} }{48} \\y = \frac{-2+-\sqrt{1444} }{48} \\y = \frac{-2+- 38}{48} \\y = \frac{-2+38}{48} \\y = \frac{3}{4}\\ \\or\\y = \frac{-2-38}{48} \\y = \frac{-40}{48} \\y = -\frac{5}{6}

From the calculations above, the solution to the equation are 3/4 and -5/6 and the greater of the two solutions is 3/4

Learn more on quadratic equation here;

brainly.com/question/8649555

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