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
crimeas [40]
2 years ago
15

If tan (x) = 24/19 (in Quadrant 1), find

Mathematics
1 answer:
Natasha2012 [34]2 years ago
6 0

If x is in quadrant I, then both sin(x) and cos(x) are positive. The angle x/2 also belongs to quadrant I, and hence each of sin(x/2), cos(x/2), and tan(x/2) are positive.

Recall that for all x,

cos²(x) + sin²(x) = 1

and multiplying through both sides by 1/cos²(x) = sec²(x) gives another flavor of this identity,

1 + tan²(x) = sec²(x)

It follows that

sec(x) = √(1 + tan²(x)) = √937/19

which immediately gives us

cos(x) = 19/√937

and from the identity above we find

sin(x) = √(1 - cos²(x)) = 24/√937

Recall the half angle identity for cos :

cos²(x) = (1 + cos(2x))/2

which means

cos(x/2) = + √[(1 + cos(x))/2] = √[1/2 + 19/(2√937)]

Then

sin(x/2) = + √(1 - cos²(x/2)) = √[1/2 - 19/(2 √937)]

and by definition of tan,

tan(x/2) = sin(x/2) / cos(x/2) = 1/12 √[649/2 - 19 √937/2]

Just to be clear, the solutions are

\cos\left(\dfrac x2\right) = \sqrt{\dfrac12 + \dfrac{19}{2\sqrt{937}}}

\sin\left(\dfrac x2\right) = \sqrt{\dfrac12 - \dfrac{19}{2\sqrt{937}}}

\tan\left(\dfrac x2\right) = \dfrac1{12} \sqrt{\dfrac{649 - 19\sqrt{937}}2}

You might be interested in
Which number is rational? 2 square root, pi ,10 square root ,16 squeare root
ki77a [65]

Answer:

Square root of 16 is rational beacuse Square root of 16=4 Whlie the others are Irational.

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
I confused on this question
Fynjy0 [20]
42 degrees. Comment down if you need the explanation why
6 0
3 years ago
Read 2 more answers
Which is the best estimate for the percent equivalent of 7/15
zzz [600]
An estimate for the percent equivalent of 7/15 is 46% i think
7 0
3 years ago
Read 2 more answers
The water park had a total of 1,212 visitors on Friday, Saturday, and Sunday. If the same number of people visited each day, how
Archy [21]
The answer is 404 visitors per day, Because 3/1212=404
5 0
3 years ago
Read 2 more answers
What is the price per pound if the can is 2 7/8 pounds and the price is $1.38
Lerok [7]

Answer:

$2.08

Step-by-step explanation:

2 7/8= 23/8 divided 1.38

7 0
3 years ago
Other questions:
  • Write 0.4% as a fraction explain
    15·2 answers
  • It takes Oliver 30 minutes to walk to school everyday a distance of 1.5 miles. what is Oliver speed in miles per hour
    9·2 answers
  • Find the volume of a cube whose surface area is 150Ft
    9·1 answer
  • Madison Middle School spends $750 per year on club activities. They spend at least twice the amount on after school activities.
    5·1 answer
  • Point A is located at the coordinates (3,5); if the point is rotated 180° about the origin, what will be the new coordinates of
    14·1 answer
  • What is the answer to 10x[9÷(8+1)]
    12·2 answers
  • Some one talk to me :(
    10·2 answers
  • What is an equation of the line that passes through the point (−6,−1) and is perpendicular to the line 6x−y=7?
    5·1 answer
  • Write the slope-intercept form of the equation of each line given the slope and y-intercept.
    15·1 answer
  • The expression 16t² represents the distance, in feet, an object falls after t seconds. The object is dropped from a height of 90
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!