# Checking this answer regarding a trig problem

• rxh140630
I get \sqrt{2}Cos(x+3pi/4) = sinx+cosxIn summary, the conversation is about proving the existence of C and ∝ with certain conditions and determining their values for given real numbers A and B. The author gave a solution of C = √2 and ∝ = -π/4, and the person asking the question suggested an alternative solution of C = -√2 and ∝ = -3π/4. Further discussion revolved around checking the validity of the alternative solution.
rxh140630
Homework Statement
Prove that if A, B are given real numbers there exists C and ∝ with C ≥ 0 such that Ccos(x+∝) = Asinx + Bcosx. Determine C and ∝ if A=B=1
Relevant Equations
cos(x+y)= cosxcosy-sinxsiny
Author gave solution $C = \sqrt{2}, ∝ = -pi/4$

but plugging $C = - \sqrt{2}, ∝ = -3pi/4$ into cos(x+y) and leaving the x I get $\sqrt{2}Cos(x+3pi/4) = sinx+cosx$

Is my answer valid as well?

rxh140630 said:
Homework Statement:: Prove that if A, B are given real numbers there exists C and ∝ with C ≥ 0 such that Ccos(x+∝) = Asinx + Bcosx. Determine C and ∝ if A=B=1
Relevant Equations:: cos(x+y)= cosxcosy-sinxsiny

Author gave solution $C = \sqrt{2}, ∝ = -pi/4$

but plugging $C = - \sqrt{2}, ∝ = -3pi/4$ into cos(x+y) and leaving the x I get $\sqrt{2}Cos(x+3pi/4) = sinx+cosx$

Is my answer valid as well?

rxh140630 said:
... with C ≥ 0 ...
...
but plugging $C = - \sqrt{2},$

## 1. How do I know if my answer for a trig problem is correct?

One way to check your answer for a trig problem is to use a calculator or trigonometric table to verify the values of the angles and sides in the problem. You can also plug your answer back into the original equation to see if it satisfies the given conditions.

## 2. Are there any common mistakes to watch out for when solving trig problems?

Some common mistakes to watch out for when solving trig problems include forgetting to convert angles from degrees to radians, using the wrong trigonometric function for a given angle, and mixing up the order of operations when simplifying expressions.

## 3. Can I use a calculator to solve trig problems?

Yes, you can use a calculator to solve trig problems. However, it is important to understand the concepts and formulas behind the calculations in order to use a calculator effectively and catch any errors that may occur.

## 4. How can I check my work when solving trig problems by hand?

To check your work when solving trig problems by hand, you can use reference angles, trigonometric identities, and the unit circle to verify your calculations. You can also compare your answer to a similar problem or use a graphing calculator to plot the trigonometric functions.

## 5. What should I do if I am still unsure if my answer for a trig problem is correct?

If you are still unsure if your answer for a trig problem is correct, you can ask a teacher or tutor for help, check your work with a classmate, or look for similar problems in textbooks or online resources to compare your answer to. It is also important to practice regularly and review any mistakes to improve your understanding of trigonometry.

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