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4 years ago

Write the expression as the sine, cosine, or tangent of an angle. sin 8x cos x - cos 8x sin x

Mathematics

2 answers:

velikii [3]4 years ago

8 0

Answer:

sin(7x)

Step-by-step explanation:

sin 8x cos x - cos 8x sin x

We use identity

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

We have 8x in the place of 'a' and x in the place of 'b'

sin(8x-x) = sin 8x cos x - cos 8x sin x

So sin(a-b) becomes sin(8x-x)

sin(8x-x) = sin(7x)

So sin 8x cos x - cos 8x sin x= sin(7x)

Otrada [13]4 years ago

4 0

Sin(8x)cos(x) - cos(8x)sin(x)

identity being used: -cos(s)sin(t) + cos(t)sin(s) = sin(s-t)
sin(8x)cos(x) - cos(8x)sin(x) --> simplified = sin(8x-x)
sin(8x-x) is simplified to --> sin (7x)
sin(8x)cos(x) - cos(8x)sin(x) = sin(7x)

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If y is the circumcenter is angle STU find each measure

snow_tiger [21]

Answer:

Measures are SV=9 units., SY=14 units, YW= $\sqrt75units$ , YW= $\sqrt27units$

Step-by-step explanation:

Given Y is the circumcenter of ΔSTU. we have to find the measures SV, SY, YW and YX.

As Circumcenter is equidistant from the vertices of triangle and also The circumcenter is the point at which the three perpendicular bisectors of the sides of the triangle meet.

Hence, VY, YW and YX are the perpendicular bisectors on the sides ST, TU and SU.

Given ST=18 units.

As VY is perpendicular bisector implies SV=9 units.

Also in triangle VTY

$YT^{2}=VY^{2}+VT^{2}$

⇒ $14^{2}=VY^{2}+9^{2}$

⇒ VY^{2}=115

As vertices of triangle are equidistant from the circumcenter

⇒ SY=YT=UY=14 units

Hence, SY is 14 units

In ΔUWY, $UY^{2}=YW^{2}+UW^{2}$

⇒ $14^{2}=YW^2+11^{2}$

⇒ $YW^2=196-121=75$ ⇒ YW= $\sqrt75units$

In ΔYXU, $UY^{2}=YX^{2}+XU^{2}$

⇒ $14^{2}=YX^2+13^{2}$

⇒ $YX^2=196-169=27$ ⇒ YW= $\sqrt27units$

Hence, measures are SV=9 units., SY=14 units, YW= $\sqrt75units$ , YW= $\sqrt27units$

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3 years ago

What is the range of g(x)?

Mila [183]

Answer:

Step-by-step explanation:

I just need for the points

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3 years ago

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mylen [45]

Answer:

11.2467

Step-by-step explanation:

First we need to find the mean

Add up all the data and divide by number of points)

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26.1

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3 years ago

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marta [7]

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