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mestny [16]
3 years ago
15

Find the exact value of the expression

Mathematics
1 answer:
Serhud [2]3 years ago
6 0

Answer:

The answer to your question is the letter C

Step-by-step explanation:

Data

sec Ф = 9/2

tan Ф = ?

To solve this problem use trigonometric functions.

1.- The first condition is that the angle must be in the fourth quadrangle

(270° < Ф < 360°).

2.- Write the trigonometric function sec.

           sec Ф = hypotenuse / adjacent side   and sec Ф = 9/2

then, hypotenuse = 9   adjacent side = 2

3.- Use the Pythagorean theorem to find the adjacent side.

           Hypotenuse² = Opposite side² + Adjacent side²

-Solve for Opposite side

            Opposite side² = Hypotenuse² - Adjacent side sie²

-Substitution

            Opposite side² = 9² - 2²

-Simplification

            Opposite side² = 81 - 4

            Opposite side² = 77

            Opposite side = √77

4.- Find the tan Ф

             tan Ф = Opposite side/Adjacent side

-Substitution

             tanФ = -√77 / 2    It is negative because in the fourth quadrangle

                                           tan is negative.

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What are the converse, inverse, and contrapositive of the following true conditional? What are the truth values of each?
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<span>In logic, the converse of a conditional statement is the result of reversing its two parts. For example, the statement P → Q, has the converse of Q → P.

For the given statement, 'If a figure is a rectangle, then it is a parallelogram.' the converse is 'if a figure is a parallelogram, then it is rectangle.'
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The inverse of a conditional statement is the result of negating both the hypothesis and conclusion of the conditional statement. For example, the inverse of P <span>→ Q is ~P </span><span>→ ~Q.
</span><span><span>For the given statement, 'If a figure is a rectangle, then it is a parallelogram.' the inverse is 'if a figure is not a rectangle, then it is not a parallelogram.'
As can be seen, the inverse statement is not true, hence the truth value of the inverse statement is false.</span>
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The contrapositive of a conditional statement is switching the hypothesis and conclusion of the conditional statement and negating both. For example, the contrapositive of <span>P → Q is ~Q → ~P. </span>
<span><span>For the given statement, 'If a figure is a rectangle, then it is a parallelogram.' the contrapositive is 'if a figure is not a parallelogram, then it is not a rectangle.'
As can be seen, the contrapositive statement is true, hence the truth value of the contrapositive statement is true.</span> </span>
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