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4 years ago

How are different ideas about geometry connected?

Mathematics

1 answer:

Margarita [4]4 years ago

8 0

They areall related to geoemtry

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use compound angle formulae to find sin 15 and cos 15 in form of [ surd a (surd b + c) ] . Hence, find tan 15 in the simplest su

inysia [295]

Answer:

see explanation

Step-by-step explanation:

Using the difference formulae for sine and cosine

sin(x - y) = sinxcosy - cosxsiny

cos(x - y) = cosxcosy + sinxsiny

sin15° = sin(45 - 30)°

sin(45 - 30)°

= sin45°cos30° - cos45°sin30°

= $\frac{\sqrt{2} }{2}$ × $\frac{\sqrt{3} }{2}$ - $\frac{\sqrt{2} }{2}$ × $\frac{1}{2}$

= $\frac{\sqrt{6} }{4}$ - $\frac{\sqrt{2} }{4}$

= $\frac{\sqrt{6}-\sqrt{2} }{4}$

----------------------------------------------------------------------------------

cos15° = cos(45 - 30)°

cos(45 - 30)°

= cos45°cos30° + sin45°sin30°

= $\frac{\sqrt{2} }{2}$ × $\frac{\sqrt{3} }{2}$ + $\frac{\sqrt{2} }{2}$ × $\frac{1}{2}$

= $\frac{\sqrt{6} }{4}$ + $\frac{\sqrt{2} }{4}$

= $\frac{\sqrt{6}+\sqrt{2} }{4}$

-------------------------------------------------------------------------------------

tan15° = $\frac{sin15}{cos15}$

= $\frac{\sqrt{6}-\sqrt{2} }{4}$ × $\frac{4}{\sqrt{6}+\sqrt{2} }$

= $\frac{\sqrt{6}-\sqrt{2} }{\sqrt{6}+\sqrt{2} }$

Rationalise the denominator by multiplying numerator/ denominator by the conjugate of the denominator, that is ( $\sqrt{6}$ - $\sqrt{2}$ )

= $\frac{(\sqrt{6}-\sqrt{2})^2 }{(\sqrt{6}+\sqrt{2})(\sqrt{6}-\sqrt{2}) }$

= $\frac{6-4\sqrt{3}+2 }{6-2}$

= $\frac{8-4\sqrt{3} }{4}$

= 2 - $\sqrt{3}$

5 0

3 years ago

8 which of the following numbers Is Irrational?

snow_tiger [21]

It’s the square root of 2 (100%)

4 0

4 years ago

A store has apples on sale for $28.00 for 8 pounds. If an apple is approximately 5 ounces, how many apples can you buy for $112.

lys-0071 [83]

Answer

101 apples

Step-by-step explanation:

8 lbs x 16 oz = 128 oz

$28 / 128 oz = 22¢ per oz

$112 / 0.22¢ = 509 oz

509 oz / 5 oz = 101.8 apples

8 0

2 years ago

Y=2x/a+2b solve for a

mina [271]

Solve for a.

y=2x/a+2b

Multiply both sides by a.

ay=2ab+2x

Add -2ab to both sides.

ay+−2ab=2ab+2x+−2ab

−2ab+ay=2x

Factor out variable a.

a(−2b+y)=2x

Divide both sides by -2b+y.

a(−2b+y) / −2b+y = 2x / −2b+y

a = 2x / −2b+y

6 0

3 years ago

Katy is 1m 18 cm tall. Beth is 112 cm tall How much taller is Katy

Sergio [31]

Answer:

Katy is 6 cm taller.

Step-by-step explanation:

Katy: 1 meter=100cm

100cm+18cm=118cm

Beth: 112cm

118cm-112cm=6cm

6 0

3 years ago