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3 years ago

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Mathematics

1 answer:

Mariulka [41]3 years ago

6 0

Answer:

make sure that your payment went through and if it didnt contact brainly about it or something like that but u dont rlly need to spend money just answer questions thats what i do :)

Step-by-step explanation:

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If a and b are two angles in standard position in Quadrant I, find cos(a+b) for the given function values. sin a=15/17and cos b=

tensa zangetsu [6.8K]

The value of $cos(a+b)$ for the angles $a$ and $b$ in standard position in the first quadrant is $-\frac{36}{85}$

We need to find the value of $cos(a+b)$ . To proceed, we need to use the compound angle formula

<h3>Cosine of a sum of two angles</h3>

The cosine of the sum of two angles $a$ and $b$ is given below

$cos(a+b)=cos(a)cos(b)-sin(a)sin(b)$

We are given

$sin(a)=\dfrac{15}{17}\\\\cos(b)=\dfrac{3}{5}$

We need to find $sin(b)$ and $cos(a)$ , using the identity

$sin^2(\theta)+cos^2(\theta)=1$

To find $sin(b)$ , note that

$sin^2(b)+cos^2(b)=1\\\\\implies sin(b)=\sqrt{1-cos^2(b)}$

substituting $\frac{3}{5}$ for $cos(b)$ in the identity, we get

$sin(b)=\sqrt{1-cos^2(b)}\\\\=\sqrt{1-\left(\dfrac{3}{5}\right)^2}=\dfrac{4}{5}$

To find $cos(a)$ , note that

$sin^2(a)+cos^2(a)=1\\\\\implies cos(a)=\sqrt{1-sin^2(a)}$

substituting $\frac{15}{17}$ for $sin(a)$ in the identity, we get

$cos(a)=\sqrt{1-sin^2(a)}\\\\=\sqrt{1-\left(\dfrac{15}{17}\right)^2}=\dfrac{8}{17}$

<h3>Find the value of cos(a+b)</h3>

We can now make use of the formula

$cos(a+b)=cos(a)cos(b)-sin(a)sin(b)$

to find $cos(a+b)$ .

$cos(a+b)=cos(a)cos(b)-sin(a)sin(b)\\\\=\dfrac{8}{17}\cdot\dfrac{3}{5}-\dfrac{15}{17}\cdot\dfrac{4}{5}=-\dfrac{36}{85}$

Learn more about sine and cosine of compound angles here brainly.com/question/24305408

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2 years ago

Each of two urns contains green balls and red balls. Urn I contains 10 green balls and 14 red

OlgaM077 [116]

Answer:

for Urn l the probability is 14 out of 24 for Urn LL the probability is 11 out of 15

Step-by-step explanation:

you add the two then take the number of

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3 years ago

A discount store buys a shipment of swing sets at a cost of $210 each. The swing sets will be sold for $609 apiece. What percent

miv72 [106K]

Answer:

65.5172

Step-by-step explanation:

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4 years ago

: Kevin is planting 15 bushes and 9 trees in rows. If he wants all the rows to be exactly the same, with no plants left over, wh

Flauer [41]

Answer:

The greatest number of rows that can be planted, and have nothing left over, would be 3

Step-by-step explanation:

Find the greatest common factor (gcf) of 15 and 9

15: 1 3 5 15

9: 1 3 9

In this case, the gcf of 15 and 9 would be 3.

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3 years ago

Read 2 more answers

Select the statements that are true for the graph of y=(x+2)2+4 .

guapka [62]

I think you probably meant <span>(x+2)^2+4 because the equation you have provided is not written in proper formatting and would actually be a straight line. However, if you meant for that second 2 to be an exponent, you now have a quadratic equation which would graph as a parabola. Remember the basic formula is y=(x-h)^2 +k where (h,k) is your vertex. So you change the sign of the number in the parenthesis, but not the number outside the parenthesis when finding the vertex. If there is a negative number in front of your equation, then the parabola is flipped upside down so the vertex would be a maximum, but if it is positive, or has nothing in front of it, then the parabola sits up like a bowl so the vertex is a minimum.</span>

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3 years ago