1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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.
You might be interested in
Write words to match expression 24 divided by 6
miv72 [106K]

twenty four divisible by six, if that what u meant . or 24÷6

3 0
3 years ago
PLEASE ANSWER ASAP The radius of the base of this right circular cone is 10 centimeters and the slant height of the cone is 25 c
vekshin1

Answer:

B.

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
How would i get the answer for this problem 973÷2
dybincka [34]

You would divide 973 by 2 and your answer would be 486.5

7 0
3 years ago
Please help me<br>this is confusing​
Mandarinka [93]

Answer:

divide 5/9 from 10/21 first then divide it again by 6/7

Step-by-step explanation:

4 0
2 years ago
What is the percentage change when a price of 10 pounds is decreased to 7 pounds n money
Reil [10]

Answer:

30%

Step-by-step explanation:

ffuffjdgjdkgxjgxlyfylti

4 0
2 years ago
Read 2 more answers
Other questions:
  • When both pipes are working together, how long does it take them to fill the tank?
    6·1 answer
  • X^2-13x=48 factoring
    14·1 answer
  • Drag each term to the correct location on the expression. each term can be used more than once, but not all terms will be used.
    10·1 answer
  • 4.1 or 4.085 greater​
    7·2 answers
  • How do I make 105 over 8 a mixed number
    9·1 answer
  • GET NAMED BRAINLIEST AND ANSWER THE RIGHT ANSWER AND GET A THANKS AND GET 30 POINTS
    14·1 answer
  • Your grandmother is in the hospital and is put on a liquid diet. After examining her chart, a mistake is found stating that her
    9·1 answer
  • A magazine subscription costs $29.88 for 12 issues or $15.24 for 6 issues. Which subscription costs more per issue? How much mor
    6·1 answer
  • Pls help me anyone! pls im so stuck here
    11·1 answer
  • Which of the following properties is shown in the equation below? 3 × ( 6 × 2 ) = ( 3 × 6 ) × 2
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!