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
soldi70 [24.7K]
3 years ago
5

Find sec theta if theta is in quadrant 4 and sin theta= -1/5

Mathematics
2 answers:
xxTIMURxx [149]3 years ago
7 0

Answer:

\sec(\theta)=\frac{5\sqrt{6}}{12}

The answer is the last one.

Step-by-step explanation:

If we are in quadrant 4, then x (cosine) is positive and y (sine) is negative.

Since cosine is positive, secant is positive because secant is the reciprocal of cosine.

So we already know the answer is not the 1st one or the 3rd one.

I'm going to use a Pythagorean Identity to find cosine value of theta.

\cos^2(\theta)+\sin^2(\theta)=1

Enter in -1/5 for \sin(\theta):

\cos^2(\theta)+(\frac{-1}{5})^2=1

Simplify a bit:

\cos^2(\theta)+\frac{1}{25}=1

Subtract 1/25 on both sides:

\cos^2(\theta)=1-\frac{1}{25}

Write 1 as 25/25 so you have a common denominator on the right hand side:

\cos^2(\theta)=\frac{25}{25}-\frac{1}{25}

\cos^2(\theta)=\frac{24}{25}

Take the square root of both sides:

\cos(\theta)=\pm \sqrt{\frac{24}{25}}

\cos(\theta)=\pm \frac{\sqrt{24}}{\sqrt{25}}

I will worry about simplifying the square root part when finding secant.

We said that cosine was positive because we were in the fourth quadrant.

\cos(\theta)=\frac{\sqrt{24}}{\sqrt{25}}

Now recall that cosine and secant are reciprocals of each other:

\sec(\theta)=\frac{\sqrt{25}}{\sqrt{24}}

Let's simplify the square part not.

Usually people hate the square root on both and also if you look at your choices none of the choice have square root on bottom.

So we are going to multiply top and bottom by \sqrt{24}. I'm going to also write 5 instead of \sqrt{25}.

\sec(\theta)=\frac{5}{\sqrt{24}} \cdot \frac{\sqrt{24}}{\sqrt{24}}

\sec(\theta)=\frac{5\sqrt{24}}{24}

Now let's simplify the square root of 24.

We know 24 is not a perfect square, but 24 does contain a factor that is a perfect square. That factor is 4.

\sec(\theta)=\frac{5\sqrt{4}\sqrt{6}}{24}.

\sec(\theta)=\frac{5(2)\sqrt{6}}{24}

\sec(\theta)=\frac{10\sqrt{6}}{24}

Now both 10 and 24 share a common factor of 2 so let's divide top and bottom by 2:

\sec(\theta)=\frac{5\sqrt{6}}{12}

The answer is the last one.

lara31 [8.8K]3 years ago
5 0

Answer:

\frac{5}{2\sqrt{6} }

Step-by-step explanation:

Since Θ is in fourth quadrant then cosΘ > 0, as is secΘ

Given

sinΘ = - \frac{1}{5}, then

cosΘ = \sqrt{1-(-1/5)^2}

         = \sqrt{1-\frac{1}{25} } = \sqrt{\frac{24}{25} } = \frac{2\sqrt{6} }{5}

Hence

secΘ = \frac{1}{\frac{2\sqrt{6} }{5} } = \frac{5}{2\sqrt{6} }

You might be interested in
Sophia took home 2/9 of the pizza that was left over from a party. The amount she took represents 1/2 of a whole pizza. The equa
andre [41]

Answer:

19/5

Step-by-step explanation:

i used a calculater

5 0
3 years ago
True or false question
Romashka [77]
The answer should be true
6 0
3 years ago
When x=1/2, what is the value of 8x-3 over x?
IgorLugansk [536]

Answer:

2

Step-by-step explanation:

(8(1/2)-3)/(1/2)

(4-3)/(1/2)

1/(1/2)

1*2

Your answer is 2, hope this helps

5 0
3 years ago
Read 2 more answers
In the function f(x) = 225 - 31.4558 In, x represents the
KengaRu [80]

Answer:

Step-by-step explanation:

8 0
3 years ago
Sally wants to purchase a new car, and its price is $35,000. Since Sally does not have enough money, she would like to get a loa
Margaret [11]

Answer:

The formula to calculate the final cost of Sally's new car:

C = 35000 x (1 + 4.5/100)^6 = 45579.1 dollar

Hope this helps!

:)

3 0
3 years ago
Other questions:
  • Postulate: If two lines intersect, then they intersect in exactly one point. true or false
    13·1 answer
  • What are the coefficient(s) in the expression: 3x+2r-7
    13·2 answers
  • $700 is invested at 4% per annum. How long will it take for the amount to reach $784?​
    11·1 answer
  • Please provide an explanation. Thanks
    15·1 answer
  • What are the answers for x, y, and z?
    13·1 answer
  • 5(y + 2/5) = -13<br><br> Solve for y<br><br> Show or explain your method
    5·2 answers
  • Solve the system. <br>y = 3x + 1 <br>-x + 2y = -3<br>​
    8·1 answer
  • Homework please help
    10·2 answers
  • I need help and please don’t lie about the answers! I’ll help you if you need any help on other stuff!
    6·1 answer
  • Which expressionis equal to9(9MPLUS3t)
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!