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Ber [7]
3 years ago
10

Given csc(A) = 60/16 and that angle A is in Quadrant I, find the exact value of sec A in simplest radical form using a rational

denominator . Someone please help me!
Mathematics
2 answers:
Katarina [22]3 years ago
6 0

Answer:

\displaystyle \sec A=\frac{65}{63}

Step-by-step explanation:

We are given that:

\displaystyle \csc A=\frac{65}{16}

Where <em>A</em> is in QI.

And we want to find sec(A).

Recall that cosecant is the ratio of the hypotenuse to the opposite side. So, find the adjacent side using the Pythagorean Theorem:

a=\sqrt{65^2-16^2}=\sqrt{3969}=63

So, with respect to <em>A</em>, our adjacent side is 63, our opposite side is 16, and our hypotenuse is 65.

Since <em>A</em> is in QI, all of our trigonometric ratios will be positive.

Secant is the ratio of the hypotenuse to the adjacent. Hence:

\displaystyle \sec A=\frac{65}{63}

expeople1 [14]3 years ago
4 0

Answer:

Step-by-step explanation:

cosec A =60/16

hypotenuse/opposite = 60/16 =15/4 (in simplest form)

therefore hypotenuse = 15 , opposite = 4  

then adjacent =? (let be x)

using pythagoras theorem to find adjacent

opposite^2 + adjacent^2 = hypotenuse^2

4^2 + x^2 = 15^2

16 + x^2 = 225

x^2 = 225 - 16

x^2 = 209

x=\sqrt{209}

sec A =hypotenuse/adjacent

=\frac{15}{\sqrt{209} }

=\frac{15}{\sqrt{209} } * \frac{\sqrt{209} }{\sqrt{209} }

=\frac{15\sqrt{209} }{209}

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Step-by-step explanation:

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You need to remember the properties of exponents: multiplication adds the exponents, division subtracts the exponents.

If you multiply two powers with the same base, the result will be the base to the sum of the powers.

If you divide two powers with the same base, the result will be the base to the difference of the powers.

In your case you will this:

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sukhopar [10]

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Step-by-step explanation:

You can use the midpoint formula to find the midpoint of point A and point B.

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Step-by-step explanation:

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uranmaximum [27]

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Step-by-step explanation:

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1.) First, multiply each side to match either y-values or x-values. (In this example, we'll use match x-values)

10x + 14y = 18 (multiplied by 2)

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2.) Then, subtract the entirety of one equation to isolate the y-value.

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