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ira [324]
3 years ago
15

This is specifically for chika

Mathematics
1 answer:
docker41 [41]3 years ago
4 0

Answer:

says the one that kept posting that stupld link ◔_◔

Step-by-step explanation:

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Sin(x)^4+ cos(x)^4=1/2
posledela
I'll assume that what was meant was \sin ^4 x + \cos ^4 x = \dfrac{1}{2}.

The exponent in the funny place is just an abbreviation:   \sin ^4 x = (\sin x)^4.

I hope that's what you meant. Let me know if I'm wrong.

Let's start from the old saw

\cos^2 x + \sin ^2x = 1

Squaring both sides,

(\cos^2 x + \sin ^2x)^2 = 1^2

\cos^4 x + 2 \cos ^2 x \sin ^2x +\sin ^4x = 1

\cos^4 x + \sin ^4x = 1 - 2 \cos ^2 x \sin ^2x

So now the original question 

\sin ^4 x + \cos ^4 x = \dfrac{1}{2}

becomes
1 - 2 \cos ^2 x \sin ^2x = \dfrac{1}{2}

4 \cos ^2 x \sin ^2x = 1

Now we use the sine double angle formula

\sin 2x = 2 \sin x \cos x

We square it to see

\sin^2 2x = 4\sin^2 x \cos^2 x = 1

Taking the square root,

\sin 2x = \pm 1

Not sure how you want it; we'll do it in degrees. 

When we know the sine of an angle, there's usually two angles on the unit circle that have that sine.  They're supplementary angles which add to 180^\circ.  But when the sine is 1 or -1 like it is here, we're looking at 90^\circ and -90^\circ, which are essentially their own supplements, slightly less messy. 

That means we have two equations:

\sin 2x = 1 = \sin 90^\circ

2x = 90^\circ + 360^\circ k \quad integer k

x = 45^\circ + 180^\circ k

or 


\sin 2x = -1 = \sin -90^\circ

2x = -90^\circ+ 360^\circ k

x = - 45^\circ + 180^\circ k

We can combine those for a final answer,

x = \pm 45^\circ + 180^\circ k \quad integer k

Check.  Let's just check one, how about

x=-45^\circ + 180^\circ = 135^\circ

\sin(135)= 1/\sqrt{2}

\sin ^4(135)=(1/\sqrt{2})^4 = 1/4

\cos ^4(135)=(-1/\sqrt{2})^4 = 1/4

\sin ^4(135^\circ) +\cos ^4(135^\circ) = 1/2 \quad\checkmark


6 0
3 years ago
56÷(7-9)^3 -24/23-5×4​
yulyashka [42]

Answer:

= −28.043478261

Step By Step Explanation

Answer From Gauth Math

7 0
3 years ago
Read 2 more answers
a 16-ounce bottle of spring water is $1.76. a 20-ounce bottle of fresh water is $2.40. which statement about the unit prices is
Darya [45]
100% sure its C hope this helps
4 0
4 years ago
Read 2 more answers
Use the Distributive Property and then Combine Like Terms (C.L.T.) to simplify: 2(3n−5)−4n+7
Annette [7]

Answer:

Step-by-step explanation:

2(3n-5)-4n+7=

6n-10-4n+7=

-3+2n

5 0
3 years ago
Read 2 more answers
A mother has one allele for color blindness and one allele for normal vision
Setler [38]

Answer:

i say 50%

Step-by-step explanation:

if there is an outcome of 2

then there is a 50% chance she either has normal visions or color blindness

5 0
4 years ago
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