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Natasha2012 [34]
3 years ago
7

Evaluate: sec(5 pie/4)

Mathematics
1 answer:
zysi [14]3 years ago
7 0

Answer:

sec(\frac{5\pi}{4})=-\sqrt{2}

Step-by-step explanation:

sec(\frac{5\pi}{4})\\\\=\frac{1}{cos(\frac{5\pi}{4})}\\ \\=\frac{1}{-\frac{\sqrt{2}}{2}}\\ \\=-\frac{2}{\sqrt{2}}\\ \\=-\frac{2\sqrt{2}}{2}\\ \\=-\sqrt{2}

It really helps to use the unit circle for solving these kinds of problems. I've attached one for your convenience. Note that a point on the unit circle, given the angle in radians, is defined as (cos\theta,sin\theta).

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An angle is drawn in standard position passing through the unit circle at (0.643,0.766). The angle in standard position θ has a
Flura [38]
<h2>Hello!</h2>

The asnwer is: Cos50° ≈ 0.643

<h2>Why?</h2>

A unit circle is a cirgle with a radius equal of 1, knowing that,  also know the following:

The angle is drawn passing trough the unit circle at (0.643,0.766) it means that:

x=0.643\\y=0.766

So,

Cos50° ≈ 0.643

We can prove that by following the next steps:

- If it's a unit circle,here is a right triangle with hypotenuse of 1,

1^{2}=x^{2}+y^{2}

1^{2}=0.643^{2}+0.766^{2}

1^{2}=0.4134 +0.5867

1=1.0001=1

- We can determine the cosine of the angle by the following formula:

cos(\alpha)=\frac{x}{hypotenuse} \\cos(\alpha)^{-1}=cos(\frac{0.643}{1})^{-1} \\\alpha=49.98

Therefore,

Cos(α)=49.98°≈50°

Also, if there is a right triangle, according to the Pythagorean Thorem:

1^{2}=(Cos(\alpha))^{2}+(Sin(\alpha))^{2} \\Cos(50)=\sqrt{1-(Sin(50))^{2}}=0.6427

Hence,

Cos50° ≈ 0.643

Have a nice day!

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3 years ago
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Answer:

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Where would you start dividing to find the quotient of 3,825/8 explain how you know
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You divide left to right so you start at the three, hope this helps.

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