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3 years ago

What expression is equal to COS B????

Mathematics

1 answer:

Murrr4er [49]3 years ago

3 0

Answer:

A/C

Step-by-step explanation:

Since the sum of the angles in a triangle equals 180°, and angle C is 90°.

That means angles A and B add up to 90°, that is, they are complementary angles. Therefore the cosine of B equals the sine of A.

We saw on the last page that sin A was the opposite side over the hypotenuse, that is, a/c. Hence, cos B equals a/c.

Your welcome! :)

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Answer:

a. closed under addition and multiplication

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c. not closed under addition and multiplication

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Step-by-step explanation:

Let A be a set of all integers divisible by 5.

Let $x,y$ ∈A such that $x=5m\,,\,y=5n$

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Let $x,y$ ∈A such that $x=2m+1\,,\,y=2n+1$ where m, n ∈ Z.

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$x+y$ ∉ A

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$Let A=\{2,5,8,11,14,...\}$

Let $x=2,y=5$ but $x+y=2+5=7$ ∉A

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$xy=2(5)=10$ ∉A

Therefore, A is not closed under addition and multiplication.

Let A = { 17n: n∈Z}

Let $x,y$ ∈ A such that $x=17n,y=17m$

Find x + y and xy

$x+y=17n+17m=17(n+m)$

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$x+y,xy$ ∈ A

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Let $x,y$ ∈ A such that $x=-1,y=1$

Find x + y

$x+y=-1+1=0$

So,

$x+y$ ∈ A

Also, if x and y are two nonzero real numbers then xy is also a non-zero real number.

Therefore, A is not closed under addition but A is closed under multiplication.

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