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
Romashka [77]
1 year ago
6

Use the tangent identity to

Mathematics
1 answer:
Lunna [17]1 year ago
5 0

Answer:

tan(x)=\frac{44\sqrt{89}}{89}

Step-by-step explanation:

tan is defined as: tan(x)=\frac{opposite}{adjacent}

sin is defined as: sin(x)=\frac{opposite}{hypotenuse}

cos is defined as: cos(x)=\frac{adjacent}{hypotenuse}

We can also define tan as: tan(x)=\frac{sin(x)}{cos(x)}

because plugging in the definitions of sin and cos in we get: tan(x)=\frac{(\frac{opposite}{hypotenuse})}{(\frac{adjacent}{hypotenuse})}\\\\tan(x)=\frac{opposite}{hypotenuse}*\frac{hypotenuse}{adjacent}\\\\tan(x)=\frac{opposite}{adjacent}

which you'll notice is the original definition of tan(x)

So using this definition of tan(x) we can use the givens sin(x) and cos(x) to find tan(x)

sin(x)=\frac{44}{45}\\\\cos(x)=\frac{\sqrt{89}}{45}\\\\tan(x)=\frac{sin(x)}{cos(x)}

plugging in sin(x) and cos(x) we get:

tan(x)=\frac{\frac{44}{45}}{\frac{\sqrt{89}}{45}}\\\\tan(x)=\frac{44}{45}*\frac{45}{\sqrt{89}}\\\\tan(x)=\frac{44}{\sqrt{89}}

We usually don't like square roots in the denominator, and from here we want to rationalize the denominator which we do by removing the square root from the denominator.

We can do this by multiplying the fraction by: \frac{\sqrt{89}}{\sqrt{89}} which doesn't change the value of the fraction since it simplifies to 1, but it gets rid of the square root in the denominator

tan(x)=\frac{44}{\sqrt{89}}*\frac{\sqrt{89}}{\sqrt{89}}\\\\tan(x)=\frac{44\sqrt{89}}{89}

You might be interested in
Which statement is true?<br> GRAPHA<br> GRAPH B
WARRIOR [948]

Answer:

Graph B is correct

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Can someone please help me ;-; this is due today
IRISSAK [1]

Answer:

The correct answer: F (Scalene) and A (Acute)

Step-by-step explanation:

F. (Scalene):  By definition, a scalene triangle is a triangle that has no equal sides, and no equal angles. This definition matches your given triangle, since it has no equal sides and angles.

A. (Acute): By definition, an acute triangle is a triangle in which all the internal angles are less than 90 degrees. This definition matches your given triangle, since all of the internal angles are less than 90 degrees.

The given triangle is not obtuse, equilateral, right, and isoceles.

It is <u>not</u> an <em>obtuse </em>triangle because none of the angles are greater than 90 degrees.

It is <u>not</u> an <em>equilateral</em> triangle because its sides are not equal.

It is <u>not</u> a <em>right</em> triangle because none of its internal angles measure 90 degrees.

And it is <u>not</u> an <em>isoceles</em> triangle because by definition, an isoceles triangle must have two equal sides. Your given triangle has no equal sides.

6 0
3 years ago
Can anyone help me on this please
My name is Ann [436]

Answer:

Step-by-step explanation:

3 0
3 years ago
Graph the system of linear equations.
balu736 [363]

Answer:

Hi, the answer should be (-4,-6)

Step-by-step explanation:

4 0
3 years ago
Solve the sequence:0,5,12,23,34____​
MrRissso [65]

Step-by-step explanation:

the answer is 49

I may not be correct

4 0
2 years ago
Other questions:
  • Which description most accurately summarizes the samples results? Help
    11·2 answers
  • You roll two fair dice, a green one and a red one. (a) What is the probability of getting a sum of 7? (Enter your answer as a fr
    13·1 answer
  • If you wanted to find reasons for why sales are higher on certain days of the week, you would be BEST advised to examine the fac
    10·1 answer
  • Write this number in scientific notation 38200000 <br> Look at attachment down below
    15·2 answers
  • Edwin went to the grocery store and bought several pounds of fruits. The fruit cost $2 per pound. He bought 2.5 pounds of apples
    15·1 answer
  • Which number has two lines of symmetry?<br><br> 101<br> 619<br> 33<br> 18 <br> not multiple answer
    12·1 answer
  • Find the volume, V, of a right circular cylinder in terms of π, if its height is 5 yards, and the radius of its base is 2 yards.
    7·1 answer
  • Pls help me I need this for my grade do all pls
    11·1 answer
  • What is the value of x in the equation below? <br> (9x – 6) = 4x + 10
    12·2 answers
  • In one lottery game, contestants pick five numbers from 1 through 23 and have to match all five for the big prize (in any order)
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!