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alexandr1967 [171]
3 years ago
14

Prove that root3 (cosec (20))-sec (20)=4

Mathematics
2 answers:
Tems11 [23]3 years ago
7 0
Root 3 /sin 20 - 1/cos 20

= (root3 cos 20 - sin 20 )/ (sin 20 cos 20)
(multiplying and dividing by 2)
=  2* (root3/2 cos 20 -1/2 sin 20)/ (sin 20 cos 20)

now sin 20 cos 20  = (2 sin 20 cos 20)/2 = (sin 40)/2
and writing root3/2 = sin 60, 1/2 = cos 60

= 2* (sin 60 cos 20 - cos 60 sin 20)/ (sin 40)/2

= 4* (sin (60-20))/sin 40

= 4* (sin 40)/sin 40
=4

Ask if any doubt in any step :)
Mashcka [7]3 years ago
3 0
Hello,

1) Rappels:

all angles are in degree.

cos(a+b)=cos(a)cos(b)-sin(a)sin(b)
2sin(a)cos(a)=sin(2a)
sin(a)=cos(90-a)
cos(30)=√3/2
sin(30)=1/2
2)
√3 cos(20)-sin(20)=2(√3/2 cos(20)-1/2 sin(20)
=2*(cos(30) *sin(20)-sin(30) sin(20))=2 cos(30+20)=2 cos(50)

sin(20) cos(20)=1/2 cos(40)=1/2 cos(50)

<span>√3 (cosec (20))-sec (20) = √3 /sin(20)-1/cos(20)
=[√3*cos(20)-sin(20)]/(sin(20)cos(20))
=2 cos(50)/ (1/2cos(50))=4

</span>

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Step-by-step explanation:

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Answer:

(a) Approximate the percent error in computing the area of the circle: 4.5%

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Step-by-step explanation:

(a)

First we need to calculate the radius from the circumference:

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I leave only one decimal as we need to keep significative figures

Now we proceed to calculate the error for the radius:

\Delta r=\frac{dt}{dc} \Delta c\\\\\frac{dt}{dc} =    \frac{1}{2 \pi } \\\\\Delta r=\frac{1}{2 \pi } (1.2)\\\\\Delta r= 0.2 cm

r = 8.9 \pm 0.2 cm

Again only one decimal because the significative figures

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A=\pi r^{2}\\A=249 cm^{2}

Then we calculate the error:

\Delta A= (\frac{dA}{dr} ) \Delta r\\\\\Delta A= 2\pi r \Delta r\\\\\Delta A= 11.2 cm^{2}

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Now we proceed to calculate the percent error:

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(b)

With the previous values and equations, now we set our error in 3%, so we just go back changing the values:

\%e =\frac{\Delta A}{A} *100\\\\3\%=\frac{\Delta A}{249} *100\\\\\Delta A =7.5 cm^{2}

Now we calculate the error for the radius:

\Delta r= \frac{\Delta A}{2 \pi r}\\\\\Delta r= \frac{7.5}{2 \pi 8.9}\\\\\Delta r= 0.1 cm

Now we proceed with the error for the circumference:

\Delta c= \frac{\Delta r}{\frac{1}{2\pi }} = 2\pi \Delta r\\\\\Delta c= 2\pi 0.1\\\\\Delta c= 0.6 cm

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Step-by-step explanation:

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