Elementary Trigonometry, Help with

In summary: You got the sign wrong! It should be:cos(A + B) = cos(A)cos(B) - sin(A)sin(B).Oh sorry. I tried it again using that but I still fail: I get arctan(25/31). Help?If you post your steps ... we can see the mistake thereafterThank you for your help! I solved it now but with the method I tried at first: I had made sloppy mistakes somewhere. Since (thanks to flora) cos(A + B) = cosAcosB - sinAsinB I got (sinA + cosAtanB)/(cosA - sinAtanB) and, calculating cosA
  • #1
stefanB
9
0
Hello, I have been trying to solve this type of question but the results of my efforts are frequently disappointing. Since this is considered elementary and simple I have no doubt that someone can help me with this:

Solve arcsin (3/5) + arctan (1/7).

What if it had said 641/19 instead of 3/5, and 3/711 instead of 1/7? My teachers guided me towards:
tan x = tan (arcsin 3/5 + arctan 1/7) =, if arcsin 3/5 = A and arctan 1/7 = B, =
sin(A + B)/cos(A + B) which I develop to [(sinAcosB + cosAsinB)/(cosAcosB + sinAsinB)].
I do not know what to do next, and I certainly do not see how this is elementary - or am I trying to solve it the wrong way? I know the answer but the method eludes me.

I apologize if above looks messy; some posts I have read contains very structured mathematical language and it seems to be in a different font - larger and bolder, but I don't know how to write that.

Thanks in advance.
 
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  • #2
cos(A + B) = cosAcosB + sinAsinB ... Is it true? Check it.

If this message is beneficial for you, send a message. If it is not, explain what you do not understand.

Also, you can use a triangle to find cosA, sinB,... since you know that sinA=3/5 because of arcsin 3/5=A
 
Last edited:
  • #3
cos(A + B) = cos(A)cos(B) + sin(A)sin(B). At least I believe it is so.
Your message was unfortunately not beneficial for me as I find your triangle hint rather vague.
 
  • #4
stefanB said:
cos(A + B) = cos(A)cos(B) + sin(A)sin(B). At least I believe it is so.
Your message was unfortunately not beneficial for me as I find your triangle hint rather vague.

You got the sign wrong! It should be:cos(A + B) = cos(A)cos(B) - sin(A)sin(B).
 
  • #5
Oh sorry. I tried it again using that but I still fail: I get arctan(25/31). Help?
 
  • #6
i don't know if you call this elementary// that
arctanx +arctany=arctan(x+y)/1-xy

you can express arcsin(3/5) in arctan
let arcsin(3/5)=A
SinA=3/5
CosA=squareroot(1-sqr(3/5))=4/5
or, TanA=(3/5)/(4/5)=3/4
A=arctan(3/4)
or arcsin(3/5)=arctan(3/4)

now

arctan(3/4)+arctan(1/7)=arctan[ {(3/4)+(1/7)} / {1-(3/4)x(1/7)} ]
=arctan[ (25/28)/(25/28) ]
=arctan(1)
=Pie/4
------------------------

or why not to use Tan(A+B)=TanA+TanB/1-TanATanB

you got arcsin(3/5)=A
n TanA=3/4
Similarly TanB=1/7

Tan(A+B)=(3/4+1/7){1-(3/4)x(1/7)}
... and the same answer..
i hope this is correct
i think you have done some calculation or tranformation mistake while solving Sin(A+B)/cos(A+B)

if you post your steps ... we can see the mistake thereafter
 
  • #7
Thank you for your help! I solved it now but with the method I tried at first: I had made sloppy mistakes somewhere. Since (thanks to flora) cos(A + B) = cosAcosB - sinAsinB I got (sinA + cosAtanB)/(cosA - sinAtanB) and, calculating cosA through (1 - sinAsinA)^½ I get that sinA + cosAtanB = cosA - sinAtanB, why x = arctan 1 which is pi/4. Thanks again!
 

1. What is elementary trigonometry?

Elementary trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It involves using the three basic trigonometric functions - sine, cosine, and tangent - to solve for unknown sides or angles in a triangle.

2. What are the three basic trigonometric functions?

The three basic trigonometric functions are sine, cosine, and tangent. These functions are used to relate the angles of a triangle to the lengths of its sides.

3. What is the Pythagorean theorem?

The Pythagorean theorem is a fundamental concept in elementary trigonometry that states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. This theorem is used to find the length of a side in a right triangle when the other two sides are known.

4. How do you find the missing side or angle of a right triangle?

To find the missing side or angle of a right triangle, you can use the trigonometric functions and the Pythagorean theorem. For example, if you know the lengths of two sides, you can use the tangent function to find the measure of the angle opposite the known sides. If you know the measure of one angle and the length of one side, you can use the sine or cosine function to find the length of the missing side.

5. How is trigonometry used in real life?

Trigonometry has many practical applications in real life, such as in architecture, engineering, navigation, astronomy, and physics. It is used to calculate distances and heights, determine angles and directions, and solve problems involving triangles and circles. It is also used in fields like computer graphics and game development to create realistic 3D images and animations.

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