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SOVA2 [1]
3 years ago
10

If sec= 5/3 and the terminal point determined by is in quadrant 4, then

Mathematics
2 answers:
alisha [4.7K]3 years ago
8 0

Answer:

C. csc(\theta)=-\frac{5}{4}

D. cos(\theta)= \frac{3}{5}

Step-by-step explanation:

First, take a look to the picture I attached you. I drew a diagram according to the data provided from the problem. From this diagram:

I=First\hspace{3} quadrant\\II=Second\hspace{3} quadrant\\III=Third\hspace{3} quadrant\\IV=Fourth\hspace{3} quadrant

a=Opposite\\b=Adjacent\\c=Hypotenuse

Now, the functions on a right triangle like this are given by:

sin(\theta)=\frac{a}{c}\hspace{15}csc(\theta)=\frac{c}{a} \\cos(\theta)=\frac{b}{c}\hspace{15}sec(\theta)=\frac{c}{b} \\tan(\theta)=\frac{a}{b}\hspace{15}cot(\theta)=\frac{b}{a}

If:

sec(\theta)=\frac{5}{3}

Then:

c=5\\b=3

Using pythagorean theorem we can find a:

c^2=a^2+b^2

Solving for a:

a^2=5^2-3^2=16\\a=\sqrt{16} =\pm4

Since the triangle is in the fourth quadrant, the value of the opposite angle is negative, hence:

a=-4

Now, let's check every option, so we can determinate which of them are true or false.

A. tan(\theta)=\frac{4}{3}

tan(\theta)=\frac{a}{b} =\frac{-4}{3} \neq \frac{4}{3}

This is incorrect.

B. sin(\theta)=-\frac{2}{5}

sin(\theta)=\frac{a}{c} =\frac{-4}{5} \neq - \frac{2}{5}

This is incorrect.

C. csc(\theta)=-\frac{5}{4}

csc(\theta)=\frac{c}{a} =\frac{5}{-4} =- \frac{5}{4}

This is correct

D. cos(\theta)= \frac{3}{5}

cos(\theta)=\frac{b}{c} =\frac{3}{5}

This is correct.

OLga [1]3 years ago
7 0
\bf sec(\theta)=\cfrac{1}{cos(\theta)}\\\\
-----------------------------\\\\
sec(\theta)=\cfrac{5}{3}\implies \cfrac{1}{cos(\theta)}=\cfrac{5}{3}\implies \cfrac{3}{5}=cos(\theta)
\\\\\\
\textit{now, }\theta\textit{ is in the 4th quadrant}

so... notice the picture below, the angle in the fourth quadrant
now... notice, the cosine is just the distance the angle makes with the x-axis
so... using the pythagorean theorem, get the opposite side, from that triangle, keeping in mind that, "y" is negative in the 4th quadrant

once you get "y", get any other trigonometry value you need :)

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Answer:

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Step-by-step explanation:

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A water tank holds 944 gallons but is leaking at a rate of 5 gallons per week. A second water tank holds 1,180 gallons but is le
podryga [215]

Answer:

59

Step-by-step explanation:

The equation is

944 - 5x = 1180 - 9x

Notice what is being said. You start with 944 gallons and take off 5 per week

You also start with 1180 gallons and take on 9 per week.

You want to know when the two are equal. The second tank is larger, but it leaks more. That's what's going to bring about equality.

Add 9x to both sides

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Subtract 944 from both sides.

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8 0
3 years ago
Please help me with this math homework thanks :)
Ivenika [448]

Place a point at (0,-5) because that is the y-intercept (the -5 on the vertical line)

Since the slope is negative two which can be re-written as -2/1 (rise/run) you go down two and to the right once or up two and to the left once, it doesn't matter which. Another point can be placed at (1,-7) or (-3,-1), it still doesn't matter which.

Then you can draw a line connecting the two points.

I hope this helps :)

Let me know if you need further explanation

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