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pochemuha
2 years ago
8

3sina-4sin4a/sin5a if a=-45 degree

Mathematics
1 answer:
Ierofanga [76]2 years ago
8 0

Given:

The given expression is:

\dfrac{3\sin a-4\sin 4a}{\sin 5a}

To find:

The value of the given expression at a=-45.

Solution:

We have,

\dfrac{3\sin a-4\sin 4a}{\sin 5a}

Substituting a=-45, we get

\dfrac{3\sin (-45)-4\sin [4(-45)]}{\sin [5(-45)]}

=\dfrac{-3\sin (45)+4\sin (180)}{-\sin (225)}

=\dfrac{-3\sin (45)+4\sin (180)}{-\sin (180+45)}

=\dfrac{-3\sin (45)+4\sin (180)}{\sin (45)}

On substituting \sin (180), we get,

=\dfrac{-3\sin (45)+4(0)}{\sin (45)}

=\dfrac{-3\sin (45)+0}{\sin (45)}

=\dfrac{-3\sin (45)}{\sin (45)}

=-3

Therefore, the value of the given expression at  a=-45 is -3.

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Step-by-step explanation:

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I hope this helps!

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7 0
2 years ago
Galena is solving the following system. 3x+2y+3z =5 7x+y +7z=-1 4x-4y-z=-3
babymother [125]

Answer:

She did not multiply equation 3 in step 2 by the correct value.

Step-by-step explanation:

Given:

3x+2y+3z=5\\7x+y+7z=-1\\4x-4y-z=-3

In order to solve this, we need to eliminate any one variable and then form a simultaneous equation with the remaining two variables. Then, we nee to solve the simultaneous equation.

Here, Galena is trying to eliminate the variable z first.

Step 1:  She multiplies equation (3) by 3 and adds it to equation (1)

Let us multiply equation (3) by 3

(4x-4y-z=-3)\times 3 = (3\times 4x)-(3\times 4y)-(3\times z)=3\times -3\\(4x-4y-z=-3)\times 3 =12x-12y-3z=-9

Now, adding this to equation 1 will cancel out z terms.

12x-12y-3z+3x+2y+3z=-9+5\\(12x+3x)+(-12y+2y)+(3z-3z)=-4\\15x-10y+0=-4

Now, she need to make one more equation in x\ and \ y.

Step 2: She multiplies equation (3) by -7 and adds it to equation (2)

Multiplying equation (3) by -7 will give,

(4x-4y-z=-3)\times -7 = (-7\times 4x)-(-7\times 4y)-(-7\times z)=-7\times -3\\(4x-4y-z=-3)\times 3 =-28x+28y+7z=21

Now, adding this to equation 2 will not cancel out z terms.

-28x+28y+7z+7x+y+7z=21-1\\(-28x+7x)+(28y+y)+(7z+7z)=20\\-21x+29y+14z=20

So, she makes mistake in step 2 as the z terms are not being cancelled.

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Answer:

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