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slamgirl [31]
2 years ago
6

Write a paragraph explaining why we celebrate easter

Mathematics
2 answers:
umka2103 [35]2 years ago
7 0

What is the reason we celebrate Easter?

Easter is celebrated by Christians as a joyous holiday because it represents the fulfillment of the prophecies of the Old Testament and the revelation of God's salvific plan for all of humankind. In commemorating the Resurrection of Jesus, Easter also celebrates the defeat of death and the hope of salvation.

garri49 [273]2 years ago
6 0

Answer: Hello!

Easter is celebrated by Christians as a joyous holiday because it represents the fulfillment of the prophecies of the Old Testament and the revelation of God's salvific plan for all of humankind. In commemorating the Resurrection of Jesus, Easter also celebrates the defeat of death and the hope of salvation. Christians celebrate Easter because they believe that Jesus Christ was resurrected three days after his execution,

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

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

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

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So now the original question 

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Now we use the sine double angle formula

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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 


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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


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