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3 years ago

Please Help me To solve this Problem

Mathematics

1 answer:

mart [117]3 years ago

3 0

You're given that φ is an angle that terminates in the third quadrant (III). This means that both cos(φ) and sin(φ), and thus sec(φ) and csc(φ), are negative.

Recall the Pythagorean identity,

cos²(φ) + sin²(φ) = 1

Multiply the equation uniformly by 1/cos²(φ),

cos²(φ)/cos²(φ) + sin²(φ)/cos²(φ) = 1/cos²(φ)

1 + tan²(φ) = sec²(φ)

Solve for sec(φ) :

sec(φ) = - √(1 + tan²(φ))

Given that cot(φ) = 1/4, we have tan(φ) = 1/cot(φ) = 1/(1/4) = 4. Then

sec(φ) = - √(1 + 4²) = -√17

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On a right triangle, to find one missing side you can use this equation
a^2 + b^2 = c^2

a and b are the sides next to the right angle, and c is the hypotenuse (side not connected to right angle).

You first need to find the length of the dotted line before finding x. This is because to be able to use the above formula, you have to know the length of two out of three of the sides.

To solve the length of the dotted line, note that it also makes a triangle with the 5 unit line and the 5 √5 unit line. You can plug these numbers into the formula.
(5)^2+b^2=(5 √5)^2
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3 years ago

Certain circle can be represented by the following equation.

kirill115 [55]

Answer:

Center of the circle is (-9, -7)

Radius of the circle = 5 units

Step-by-step explanation:

Given question is incomplete: here is the complete question.

Certain circle can be represented by the following equation. x^2+y^2+18x+14y+105=0.

What is the center of this circle ?

What is the radius of this circle ?

Since equation of the circle has been given by the equation,

x² + y² + 18x + 14y + 105 = 0

Now we will convert this equation to the standard form of the circle.

x² + 18x + y² + 14y = -105

[x² + 2(9)x] + [y² + 2(7)x] = -105

[x² + 2(9)x + 9²] + [y² + 2(7)y + 7²] = 9² + 7² - 105

(x + 9)² + (y + 7)² = 81 + 49 - 105

(x + 9)² + (y + 7)² = 25

(x + 9)² + (y + 7)² = 5²

By comparing this equation with the standard equation of the circle → (x - h)² + (y - k)² = r²

Center of the circle is (-9, -7) and radius of the circle is 5 units.

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