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laiz [17]
3 years ago
6

If a vertical line is dropped from the x-axis to the point (12, –9) in the diagram below, what is the value of sec?

Mathematics
2 answers:
dem82 [27]3 years ago
5 0

Answer:

Value of \sec \theta = \frac{5}{4}

Step-by-step explanation:

Given: A vertical line is dropped from the x-axis to the point (12, -9) as shown in the diagram below;

To find the value of \sec \theta.

By definition of secants;

\sec \theta = \frac{1}{\cos \theta}

Now, first find the cosine of angle \theta

As the point (12 , -9) lies in the IV quadrant , where \cos \theta > 0

Consider a right angle triangle;

here, Adjacent side = 12 units and Opposite side = -9 units

Using Pythagoras theorem;

(Hypotenuse side)^2= (12)^2 + (-9)^2 = 144 + 81 = 225

or

Hypotenuse = \sqrt{225} =15 units

Cosine ratio is defined as in a right angle triangle, the ratio of adjacent side to hypotenuse side.

\cos \theta = \frac{Adjacent side}{Hypotenuse side}

then;

\cos \theta = \frac{12}{15} = \frac{4}{5}

and

\sec \theta = \frac{1}{\cos \theta}= \frac{1}{\frac{4}{5}} = \frac{5}{4}

therefore, the value of \sec \theta is, \frac{5}{4}

Debora [2.8K]3 years ago
3 0

Answer:

B

Step-by-step explanation:

took the test

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