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RideAnS [48]
3 years ago
7

Find the exact values of the six trigonometric functions of θ if θ is in standard position and the terminal side of θ is in the

specified quadrant and satisfies the given condition.
III; parallel to the line
5y − 2x + 1 = 0
Mathematics
2 answers:
mixer [17]3 years ago
7 0
5y - 2x + 1 = 0.
5y = 2x-1.

y = 2/5 x - 2/5

this tells us that tan(theta) = 2/5
sin(theta)/sqrt(1-sin^2(theta)) = 2/5
x/sqrt(1-x^2)=2/5
x^2/(1-x^2)=4/25
25x^2=4-4x^2
29x^2=4
x^2=4/29
x = -2/sqrt(29) because quadrant III
cos(x) = sqrt(1-4/29) = -5/sqrt(29)


tan(theta)=2/5
cos(theta)=-5/sqrt(29)
sin(theta)=-2/sqrt(29)
cot(theta)=5/2
sec(theta)=-sqrt(29)/5
csc(theta)=-sqrt(29)/2
Pani-rosa [81]3 years ago
7 0
So the equation of the line is 5y -2x + 1 = 0.

Let's put that in standard form (by solving for y):

5y -2x + 1 = 0
5y = 2x - 1 ~ we added 2x and subtracted 1 from both sides
y =  \frac{2}{5}x - \frac{1}{5} ~ divide both sides by 5

So now we have it in the standard form which is y = mx + b.

The m gives us the slope. Recall that slope is rise over run.

So the slope is \frac{2}{5}, which means that you could draw a triangle with a rise of 2 and a run of 5.

That's almost enough information to find the trig values, but we still need to know the hypotenuse. Well, thanks to the magic of the Pythagorean Theorem:

hyp =  \sqrt{2^2 + 5^2} =  \sqrt{4+25} =  \sqrt{29}

Alright, now that we know all three sides, we can find the values.

The "rise" (vertical) or opposite: 2
The "run" (horozontial) or adjacent: 5
The hypotenuse: \sqrt{29}

Remember SOHCAHTOA. In order from that mnemonic: 

sin(θ) = opposite over hypotenuse = \frac{2}{\sqrt{29}}

cos(θ) = adjacent over hypotenuse = \frac{5}{\sqrt{29}}

tan(θ) = opposite over adjacent = \frac{2}{5}

Now the others (cosecant, secant, and cotangent) are just the reciprocals (upside-downs) of the others. Remember that cosecant comes first (since sine comes first in the "usuals".

csc(θ) = \frac{\sqrt{29}}{2}

sec(θ) = \frac{\sqrt{29}}{5}

cot(θ) = \frac{5}{2}

We don't have to 'solve' (approximate) that square root in any of the answers since the problem asked for the exact solution.
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Add 0.0025 kg, 1750 mg, 2.25 g, and 825,000 μg, and express the answer in grams.
kozerog [31]

Answer:

6.75g

Step-by-step explanation:

The first step is converting everything to grams, by rules of three. Then we add.

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too.

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease.

Unit conversion problems, like this one, is an example of a direct relationship between measures.

First step: 0.0025kg to g

Each kg has 1000g, so:

1kg - 1000g

0.0025kg - xg

x = 1000*0.0025 = 2.5g

0.0025kg = 2.5g

Second step:  1750 mg

Each g has 1000mg, so:

1g - 1000mg

xg - 1750mg

1000x = 1750

x = \frac{1750}{1000}

x = 1.75g

1750 mg = 1.75g

2.25g - OK

Third step: 825,000 μg to g

Each g has 1,000,000 ug, so:

1g - 1,000,000 ug

xg - 825,000 ug

1,000,000x = 825,000

x = \frac{825,000}{1,000,000}

x = 0.25g

825,000 μg = 0.25g

Final step: adding everyting

0.25g + 2.25g + 1.75g + 2.50g = 6.75g

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Answer:

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Step-by-step explanation:

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Frankie and Maria paid to get into the carnival, and they had to pay a certain amount per game. Frankie played 5 games and spent
Natali [406]

Answer:

It cost $8 per person to get into the carnival

Step-by-step explanation:

Let the entry cost be y

Let Cost of 1 game be x

Cost of 5 games = 5x

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So, 5x+y=15.50 --- A

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So, 12x+y=26 -- B

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