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3 years ago

Find the exact value of cos 45º in simplest form with a rational denominator.

Mathematics

1 answer:

goldenfox [79]3 years ago

8 0

Answer:

$\frac{\sqrt{2} }{2}$

Step-by-step explanation:

Cos is Adjacent over Hypotenuse, (see picture below)

x/xsqrt(2)

1/sqrt(2)

sqrt(2)/2

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3 years ago

Using a linear approximation, estimate f(2.1), given that f(2) = 5 and f'(x) = √3x-1.

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$f\left( {2.1} \right) \approx 5.22360$ .

Step-by-step explanation:

The linear approximation is given by the equation

${f\left( x \right) \approx L\left( x \right) }={ f\left( a \right) + f^\prime\left( a \right)\left( {x - a} \right).}$

Linear approximation is a good way to approximate values of $f(x)$ as long as you stay close to the point $x= a$ , but the farther you get from $x=a$ , the worse your approximation.

We know that,

$a=2\\f(2) = 5\\f'(x) = \sqrt{3x-1}$

Next, we need to plug in the known values and calculate the value of $f(2.1)$ :

${L\left( x \right) = f\left( 2 \right) + f^\prime\left( 2 \right)\left( {x - 2} \right) }=5+\sqrt{3(2)-1}(x-2) =5+\sqrt{5}(x-2)$

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3 years ago

Find the exact value of cos 45º in simplest form with a rational denominator.​

Find the exact value of cos 45º in simplest form with a rational denominator.