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3 years ago

Given that tan theta = -4/7, and 270° < theta < 360°, what is the exact value of sec theta

Mathematics

1 answer:

aleksley [76]3 years ago

6 0

Answer:

sec Θ = $\frac{\sqrt{65} }{7}$

Step-by-step explanation:

Using the trigonometric identity

sec²Θ = tan²Θ + 1

Since 270° < Θ < 360° ← that is fourth quadrant, then

sec Θ > 0, thus

sec²Θ = (- $\frac{4}{7}$ )² + 1 = $\frac{16}{49}$ + 1 = $\frac{65}{49}$ , then

sec Θ = $\sqrt{\frac{65}{49} }$ = $\frac{\sqrt{65} }{7}$

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3 years ago

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4 years ago

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3 years ago

Polygon D is a scaled copy of polygon C using a scale factors of 6

Vladimir79 [104]

Answer: The area of the Polygon D is 36 times larger than the area of the Polygon C.

Step-by-step explanation:

<h3> The complete exercise is: "Polygon D is a scaled copy of Polygon C using a scale factor of 6. How many times larger is the area of Polygon D than the area Polygon C"?</h3>

In order to solve this problem it is important to analize the information provided in the exercise.

You know that the Polygon D was obtained by multiplying the lengths of the Polygon C by the scale factor of 6.

Then, you can identify that the Length scale factor used is:

$Length\ scale\ factor=k=6$

Now you have to find the Area scale factor.

Knowing that the Length scale factos is 6, you can say that the Area scale factor is:

$Area \ scale\ factor=k^2=6^2$

Finally, evaluating, you get that this is:

$Area \ scale\ factor=36$

Therefore, knowing the Area scale factor, you can determine that the area of the Polygon D is 36 times larger than the area of the Polygon C.

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4 years ago

Given that tan theta = -4/7, and 270° < theta < 360°, what is the exact value of sec theta​

Given that tan theta = -4/7, and 270° < theta < 360°, what is the exact value of sec theta