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4 years ago

15

Use a right triangle to write the following expression in algebraic expression. Assume that x is positive and in the domain of t

he given inverse trigonometric function.tan(cos−1(9x))=

1 answer:

grin007 [14]4 years ago

5 0

Answer:

The algebraic expression for $tan(cos^{-1}(9x))=\frac{\sqrt{1-81x^{2}}}{9x}$

Step-by-step explanation:

Let θ = $cos^{-1}(9x)$ use the properties of inverse trigonometric functions $cos(\theta)=cos(cos^{-1}(\theta))=\theta\\cos(\theta)=cos(cos^{-1}(9x))=9x$

In a right angled triangle, the cosine of an angle is

$cos(\theta)=\frac{adjacent}{hypotenuse}$

Use this expression $cos(\theta)=9x$ to find what are the sides of the right triangle.

$cos(\theta)=\frac{adjacent}{hypotenuse}\\cos(\theta)=\frac{9x}{1}$

Next find what is the expression for the opposite side, for this use the Pythagorean theorem and the values above

$opposite^{2}+adjacent^{2}=hypotenuse^{2}\\opposite^{2}= hypotenuse^{2}-adjacent^{2}\\opposite =\sqrt{1-81x^{2}}$

We said that $\theta = cos^{-1}(9x)$ , so now we can use the definition of tangent $tangent(\theta)=\frac{opposite}{adjacent}$ and the right triangle that we defined to find the algebraic expression for

$tan(cos^{-1}(9x))$

$tan(cos^{-1}(9x))=tan(\theta) \\ tan(\theta)=\frac{\sqrt{1-81x^{2}}}{9x}$

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4 years ago

Read 2 more answers

PLEASE HELP QWQ AsAp with these 4 questions

den301095 [7]

Answer:

Step-by-step explanation:

I can't believe I'm doing this for 5 points, but ok!

For the first 3, we are going to multiply to find the value of that 3 x 3 matrix by picking up the first 2 columns and plopping them down at the end and then multiplying through using the rules for multiplying matrices:

$\left[\begin{array}{ccccc}7&4&6&7&4\\-4&8&9&-4&8\\1&8&7&1&8\end{array}\right]$ and from there find the sum of the products of the main axes minus the sum of the products of the minor axes, as follows (I'm not going to state the process in the next 2 problems, so make sure you follow it here. This is called the determinate. The determinate is what you get when you evaluate or find the value of a matrix. Just so you know):

$(7*8*7)+(4*9*1)+(6*-4*8)-[(1*8*6)+(8*9*7)+(7*-4*4)]$ which gives us:

392 + 36 - 192 - [48 + 504 - 112] which simplifies to

236 - 440 which is -204

On to the second one:

$\left[\begin{array}{ccccc}-8&-4&-1&-8&-4\\1&7&-3&1&7\\8&9&9&8&9\end{array}\right]$ and multiplying gives us

$(-8*7*9)+(-4*-3*8)+(-1*1*9)-[(8*7*-1)+(9*-3*-8)+(9*1*-4)]$ which gives us:

-504 + 96 - 9 - [-56 + 216 - 36] which simplifies to

-417 - 124 which is -541, choice c.

Now for the third one:

$\left[\begin{array}{ccccc}-2&-2&-5&-2&-2\\2&7&-3&2&7\\8&9&9&8&9\end{array}\right]$ and multiplying gives us

$(-2*7*9)+(-2*-3*8)+(-5*2*9)-[(8*7*-5)+(9*-3*-2)+(9*2*-2)]$ which gives us:

$-126+48-90-[-280+54-36]$ which simplifies to

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Find the inverse by:

* finding the determinate

* putting the determinate under a 1

* multiply that by the "mixed up matrix (you'll see...)

First things first, the determinate:

|A| = (-4*-8) - (-6*-5) which simplifies to

|A| = 32 - 30 so

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x = 20 - 5 which is

x = 15 and

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Evgen [1.6K]

Answer:

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4 years ago

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jok3333 [9.3K]

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4 years ago