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If 180° < α < 270°, cos⁡ α = −817, 270° < β < 360°, and sin⁡ β = −45, what is cos⁡ (α + β)?

eduard

Answer:

$cos(\alpha+\beta)=-\frac{84}{85}$

Step-by-step explanation:

we know that

$cos(\alpha+\beta)=cos(\alpha)*cos(\beta)-sin(\alpha)*sin(\beta)$

Remember the identity

$cos^{2} (x)+sin^2(x)=1$

step 1

Find the value of $sin(\alpha)$

we have that

The angle alpha lie on the III Quadrant

so

The values of sine and cosine are negative

$cos(\alpha)=-\frac{8}{17}$

Find the value of sine

$cos^{2} (\alpha)+sin^2(\alpha)=1$

substitute

$(-\frac{8}{17})^{2}+sin^2(\alpha)=1$

$sin^2(\alpha)=1-\frac{64}{289}$

$sin^2(\alpha)=\frac{225}{289}$

$sin(\alpha)=-\frac{15}{17}$

step 2

Find the value of $cos(\beta)$

we have that

The angle beta lie on the IV Quadrant

so

The value of the cosine is positive and the value of the sine is negative

$sin(\beta)=-\frac{4}{5}$

Find the value of cosine

$cos^{2} (\beta)+sin^2(\beta)=1$

substitute

$(-\frac{4}{5})^{2}+cos^2(\beta)=1$

$cos^2(\beta)=1-\frac{16}{25}$

$cos^2(\beta)=\frac{9}{25}$

$cos(\beta)=\frac{3}{5}$

step 3

Find cos⁡ (α + β)

$cos(\alpha+\beta)=cos(\alpha)*cos(\beta)-sin(\alpha)*sin(\beta)$

we have

$cos(\alpha)=-\frac{8}{17}$

$sin(\alpha)=-\frac{15}{17}$

$sin(\beta)=-\frac{4}{5}$

$cos(\beta)=\frac{3}{5}$

substitute

$cos(\alpha+\beta)=-\frac{8}{17}*\frac{3}{5}-(-\frac{15}{17})*(-\frac{4}{5})$

$cos(\alpha+\beta)=-\frac{24}{85}-\frac{60}{85}$

$cos(\alpha+\beta)=-\frac{84}{85}$

4 0

3 years ago

What is the recursive rule for this geometric sequence? 1/2, -2, 8, -32

Gnesinka [82]

Answer:

see explanation

Step-by-step explanation:

A recursive rule allows us to find the term in a sequence from the previous term.

From the given geometric sequence find r the common ratio

r = $\frac{-2}{\frac{1}{2} }$ = $\frac{8}{-2}$ = - 4

Hence recursive rule is

$a_{n+1}$ = - 4 $a_{n}$ ( a₁ = $\frac{1}{2}$ )

4 0

3 years ago

Equations

Flauer [41]

Answer:

Step-by-step explanation:

-3x + 4y = -18

8x - 4y = 28

5x = 10

x = 2

4 - y = 7

-y = 3

y = -3

(2, -3)

8 0

3 years ago

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Prove: An even plus an even is<br> an even<br> 2n + 2m = [? ](n + m)<br> = even

KonstantinChe [14]

Answer:

2(n + m)

Step-by-step explanation:

3 0

2 years ago

The probability of a biased coin landing on heads is 2/7 complete the tree diagram

mamaluj [8]

Answer:

The numbers needed to fill each box are in the image attached

Step-by-step explanation:

The probability of the coin landing on heads is 2/7, so the probability of it landing on tails is 1 - 2/7 = 5/7

The probability of landing heads 2 times is:

P = (2/7) * (2/7) = 4/49

The probability of landing heads and then tails is:

P = (2/7) * (5/7) = 10/49

The probability of landing tails and then heads is:

P = (5/7) * (2/7) = 10/49

The probability of landing tails 2 times is:

P = (5/7) * (5/7) = 25/49

The numbers needed to fill each box are in the image attached.

8 0

3 years ago

Read 2 more answers