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olga55 [171]
2 years ago
12

The cosine of 23° is equivalent to the sine of what angle

Mathematics
1 answer:
Archy [21]2 years ago
6 0

Answer:

So 67 degrees is one value that we can take the sine of such that is equal to cos(23 degrees).

(There are more values since we can go around the circle from 67 degrees numerous times.)

Step-by-step explanation:

You can use a co-function identity.

The co-function of sine is cosine just like the co-function of cosine is sine.

Notice that cosine is co-(sine).

Anyways co-functions have this identity:

\cos(90^\circ-x)=\sin(x)

or

\sin(90^\circ-x)=\cos(x)

You can prove those drawing a right triangle.

I drew a triangle in my picture just so I can have something to reference proving both of the identities I just wrote:

The sum of the angles is 180.

So 90+x+(missing angle)=180.

Let's solve for the missing angle.

Subtract 90 on both sides:

x+(missing angle)=90

Subtract x on both sides:

(missing angle)=90-x.

So the missing angle has measurement (90-x).

So cos(90-x)=a/c

and sin(x)=a/c.

Since cos(90-x) and sin(x) have the same value of a/c, then one can conclude that cos(90-x)=sin(x).

We can do this also for cos(x) and sin(90-x).

cos(x)=b/c

sin(90-x)=b/c

This means sin(90-x)=cos(x).

So back to the problem:

cos(23)=sin(90-23)

cos(23)=sin(67)

So 67 degrees is one value that we can take the sine of such that is equal to cos(23 degrees).

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2 years ago
John has decided to prepare an old field for his son's new horse. the length of the field is 10 meters less than 4 times its wid
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Answer: The total money invested in the field will be $1,623.80

Step-by-step explanation:

step 1

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Let

x -----> the length of the field

y -----> the width of the field

p=2(x+y)

p(4.80)=1,584

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we know that

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so

330=2(x+y)----> equation A

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substitute equation B in equation A and solve for y

330=2(4y-10+y)

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therefore

The length of the field is 130 meters and the width of the field is 35 meters

step 2

Find the area of the field

The area of the field is

A=xy

substitute

A=(130)(35)=4,550m2

step 3

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Divide the area by 460

4,550/460=9.89 bags

Round up to the nearest whole number

9.89 bags=10 bags

step 4

Find the cost of the seed

(10 )(3.98)=$19.8

step 5

Find the total money invested in the field

1,584+$39.8=$1,623.80

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