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
galina1969 [7]
3 years ago
12

If sin(x) = 5/13, and x is in quadrant 1, then tan(x/2) equals what?

Mathematics
1 answer:
Rufina [12.5K]3 years ago
4 0
x is in quadrant I, so 0, which means 0, so \dfrac x2 belongs to the same quadrant.

Now,

\tan^2\dfrac x2=\dfrac{\sin^2\frac x2}{\cos^2\frac x2}=\dfrac{\frac{1-\cos x}2}{\frac{1+\cos x}2}=\dfrac{1-\cos x}{1+\cos x}

Since \sin x=\dfrac5{13}, it follows that

\cos^2x=1-\sin^2x\implies \cos x=\pm\sqrt{1-\left(\dfrac5{13}\right)^2}=\pm\dfrac{12}{13}

Since x belongs to the first quadrant, you take the positive root (\cos x>0 for x in quadrant I). Then

\tan\dfrac x2=\pm\sqrt{\dfrac{1-\frac{12}{13}}{1+\frac{12}{13}}}

\tan x is also positive for x in quadrant I, so you take the positive root again. You're left with

\tan\dfrac x2=\dfrac15
You might be interested in
Jamal earns $2200 each month and has a car payment of $264. What percent of his income goes toward his car payment?
finlep [7]

2200 / 264 = 8.333333-

Round the answer, which is 8.

So, your answer is A. 8%

3 0
3 years ago
Which is less 2.5 or -2.5? Answer asap pls!
masha68 [24]

its definitely -2.5........

4 0
3 years ago
Cedric opened a new gallon jug of milk and poured ¾ cup of milk for his mom, ½ cup milk for his little sister and 2 cups of milk
julia-pushkina [17]

Answer:

12 _3/4

Step-by-step explanation:

3/4 + 1/2 + 2 = 3_1/4

16 cups in a gallon

16-3_1/4

=12_3/4

7 0
3 years ago
TRUE OR FALSE <br>becomes zero for x=1<br>PLEASE HELP​<br>​
dem82 [27]

Answer:

False

Step-by-step explanation:

x is 1 not zero

5 0
2 years ago
2/3 x 2 1/3 = what is the awsner to this
topjm [15]

Answer:

1 5/9

Step-by-step explanation:

3 0
3 years ago
Other questions:
  • What is the point of intersection of the x-axis and the y-axis called?
    7·2 answers
  • Y=-3x 2.5 is it linear
    15·2 answers
  • Find the product y 4 · y 5
    8·2 answers
  • Matthew is shopping for shoes and socks. He has $75.00 to spend. The shoes he likes cost $28.00, and the socks cost 4.00. Write
    9·2 answers
  • HELP PLEASE!<br> Thankkkkkk youuuuu❤️
    10·1 answer
  • In ΔDFE, which trigonometric ratio has the same value as sin D?
    15·2 answers
  • Write out the equation (1,-19),(-2,-7)
    5·1 answer
  • There are 85 girls and 70 boys in the sixth grade. Of these students, 14
    12·1 answer
  • A pickup truck travels 45 Mi on 2 and 1/3 gallons of gas how far did it travel on 1 gallon of gas
    13·2 answers
  • Determine whether the following scenario represents a direct variation and describe why or why not: It takes 4 painters 8 hours
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!