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
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 :)

You might be interested in
Function: y = x^2+ 5x - 7 <br> Vertex:( <br> Solutions:( <br> and
tino4ka555 [31]

Answer:

Vertex: (-\frac{5}{2} , -\frac{53}{4})

Solutions: (0,-7), (1, -1), (2, 7)

I hope this helps!

8 0
3 years ago
Answers to 5 and 6 please need help please!
Tresset [83]

My friend says 5 is 60 and 6 is b.

8 0
3 years ago
What does this mean from the Declaration of Independence
vampirchik [111]
If you don't know what the Declaration of Independence means:
The Declaration of Independence is the statement adopted by the Second Continental Congress meeting at the Pennsylvania State House (Independence Hall) in Philadelphia on July 4, 1776, which announced that the thirteen American colonies,[2] then at war with the Kingdom of Great Britain, regarded themselves as thirteen newly independent sovereign states, and no longer under British rule. Instead they formed a new nation—the United States of America. John Adams was a leader in pushing for independence, which was passed on July 2 with no opposing vote cast. A committee of five had already drafted the formal declaration, to be ready when Congress voted on independence. The term "Declaration of Independence" is not used in the document itself
I hope that helps
7 0
3 years ago
Which of the following sets is closed under multiplication? {0, 1, 2, 4} {0, 1} {1, 2}
emmasim [6.3K]
It would be {0,1} :)
3 0
3 years ago
principle is used to find the number of strings of eight uppercase English letters that start or end with the letters BO (in tha
yKpoI14uk [10]
There are 6 other positions in the string, each with 26 choices. So if you fix BO as the first two letters, there are 26^6 possible strings that you can make.

If BO is at the end of the string, you still have 26^6 possible strings.

Together, then, you have 2\times26^6 possible strings.
5 0
3 years ago
Other questions:
  • Find the volume of a box with length 25 cm, height 25 cm and width 1.0 m.
    5·1 answer
  • Classify each triangle as equilateral isosceles or scalene ​
    15·1 answer
  • Someone please help me!
    10·1 answer
  • I will GIVE U Braniest!
    13·2 answers
  • before school rafael jogs laps around the school. it takes him an average of 8 minutes to jog around the school once, and then i
    9·1 answer
  • What is equivalent <br> to 2x-7(6)
    12·1 answer
  • A car can travel 65 miles in 1 hour. If the car continues at that speed for 12 hours, how many miles will it travel? (please sho
    13·2 answers
  • Q:
    5·1 answer
  • Shhsgxjabahwhdsbsn d a
    9·1 answer
  • Find the slope on any given line please see attached photo
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!