Calculate Sin(A+B) with CosA= 1/3 and SinB=1/4: Check My Work

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In summary, the conversation discusses a question about calculating the sine of two given angles, A and B, where A and B fall within specific ranges. The solution involves using the trigonometric identity for sine of the sum of two angles and finding the values of sine and cosine for A and B. The conversation also notes that the notation used in the solution is incorrect and offers a correct answer.
  • #1
majinknight
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Ok So i finished my questions and was wondering if someone could check my work to see if i did it right.
Question: If CosA= 1/3, with 0<A<pie/2, and SinB=1/4, with pie/2<B<pie, Calculate sin(A+B)

My Solution:

Sin(A+B)= SinACosB + CosASinB
=SinACosB + (1/3)(1/4)
SinACosB + 1/12

Ok Now i drew Triangle A and labeled the bottom 1 and hypotaneous 3. Then used the theorum to get the last side is square root 8.
I made Triangle B and labelled hypotaneous 4, adjacent side being 1 and used theorum to get the opposite side to be square root of 15.

=(square root8/3)(square root15/4) +1/12
=(square root120/12) + 1/12
to get my final answer of squareroot 120 +1 /12.

Is that correct?
 
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  • #2
Ouch! Your trigonometry is excellent- your notation is horrible!

You are exactly right (and for the right reasons!) that
sin(A+B)= =(&radic;(8)/3)(&radic;(15)/4) +1/12

but then you seem to have lost control of your parentheses.

sin(A+ B)= &radic(120)/12+ 1/12
= (&radic(120)+ 1)/12

which is not the same as &radic(120)+ 1/12 which is how I would have interpreted "squareroot 120 +1 /12".

It's not your use of "squareroot" instead of &radic; I am complaining about- it's your use of parentheses.

(squareroot(120)+ 1)/12 would be a correct answer.
 
  • #3
shouldn't cosB be negative for [tex] \frac{\pi}{2}<B< \pi [/tex]
 

FAQ: Calculate Sin(A+B) with CosA= 1/3 and SinB=1/4: Check My Work

How do I calculate Sin(A+B)?

The formula for calculating Sin(A+B) is Sin(A)Cos(B) + Cos(A)Sin(B). You can also use a calculator or online tool to find the value of Sin(A+B).

What is the purpose of calculating Sin(A+B)?

Calculating Sin(A+B) is useful in many applications, including trigonometry, physics, and engineering. It can help solve problems involving angles and vectors.

How do I know if my Sin(A+B) calculation is correct?

You can use a calculator or online tool to check your work. You can also use the unit circle to estimate the value of Sin(A+B) and see if it aligns with your calculation.

Are there any common mistakes when calculating Sin(A+B)?

One common mistake is forgetting to use the correct formula. Make sure to double-check the formula and input the correct values for A and B. Another mistake is not using the correct units for angles (degrees or radians).

Can I use the same method to calculate Sin(A+B) for any values of A and B?

Yes, the formula for calculating Sin(A+B) can be used for any values of A and B, as long as the units for angles are consistent (degrees or radians).

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