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slavikrds [6]
3 years ago
9

The function r(n) = 5n² + 1 represents the value of the nth term in a sequence.

Mathematics
1 answer:
umka21 [38]3 years ago
7 0

Step-by-step explanation:

a_n=5n²+1

➜a_1=5(1)²+1

➜5×1+1

➜5+1

<h3>➜6</h3>

➜a_3=5(3)²+1

➜5×9+1

➜45+1

<h3>➜46</h3>
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<h3>Answer: 24/25</h3>

=================================================

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Sine is given to be negative, and so is tangent. This only happens in quadrant Q4

Recall that y = sin(theta), so if sin(theta) < 0, then we're below the x axis.

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Draw a right triangle as shown below in the attached image. We have AC = 25 and BC = 7. Use the pythagorean theorem to find that AB = 24

So this is what your steps may look like

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So because AB = 24, we know that the cosine of the angle is adjacent/hypotenuse = 24/25

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

As an alternative, you could use the trig identity

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

and plug in the given value of sine to solve for cosine. The cosine value result will be positive since we're in Q4.

So,

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

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cos^2(x) = 1 - (49/625)

cos^2(x) = (625/625) - (49/625)

cos^2(x) = (625-49)/625

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cos(x) = sqrt(576/625)

cos(x) = sqrt(576)/sqrt(625)

cos(x) = 24/25

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