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3 years ago

Which trigonometric functions are negative in the fourth (IV) quadrant?

Mathematics

1 answer:

anzhelika [568]3 years ago

7 0

<h3>Answers are: sine, tangent, cosecant, cotangent</h3>

Explanation:

On the unit circle we have some point (x,y) such that x = cos(theta) and y = sin(theta). The sine corresponds to the y coordinate of the point on the circle. Quadrant IV is below the x axis which explains why sine is negative here, since y < 0 here.

Since sine is negative, so is cosecant as this is the reciprocal of sine

csc = 1/sin

In quadrant IV, cosine is positive as x > 0 here. So the ratio tan = sin/cos is going to be negative. We have a negative over a positive when we divide.

Because tangent is negative, so is cotangent.

The only positive functions in Q4 are cosine and secant, which is because sec = 1/cos.

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3 years ago

An urn contains six red balls and four green balls. A sample of seven balls is selected at random.

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Green: 4

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3 years ago

A square rug has an inner square in the center. The side length of the inner square is x inches and the width of the outer regio

Gwar [14]

Answer: area of the outer part of the rug= 16 -x²

Step-by-step explanation:

Hi, to answer this question we have to apply the next formula:

Area of a square: Side²

Since the area of the rug including the inner square is:

Area of the rug = 4² =16 in²

And the area of the inner square is equal to:

Area if the inner square = x²

To obtain the area of the outer part of the rug we have to subtract the area of the inner square to the area of the rug.

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Feel free to ask for more if needed or if you did not understand something.

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3 years ago

Marty is taking piano lessons. She is going to practice every afternoon. The 1st week she practiced for 11 minutes each day. The

defon

Answer:

$m=7w+4$

Step-by-step explanation:

<u>Linear Modeling</u>

It consist is setting up a linear relationship between two variables, given some experimental data. Only 2 points are needed to set up the equation of a line, but if more than 2 points are used, then the result should use statistical approaches like linear regression to find the best-fit line.

For the question at hand, Marty practices his piano lessons 11 minutes the week #1. It provides the first point (1,11). He practices 25 minutes per day on the third week. It gives us another point (3,25). This is enough to find the equation of a line. The general formula for a line, having two points (m1,w1) (m2,w2) is

$\displaystyle m-m_1=\frac{m_2-m_1}{w_2-w_1}(w-w_1)$

Let's plug in our values

$\displaystyle m-11=\frac{25-11}{3-1}(w-1)$

Simplifying:

$m-11=7w-7$

$\boxed{m=7w+4}$

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4 years ago