- #1
afrocod
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Homework Statement
sin (90 - θ + λ)
= sin90cos(θ + λ) - cos90sin(θ + λ)
= cos(θ + λ)
The book says cos(θ - λ)
So are we both right and if so how can I manipulate mine to look like the books answer.
Sine of sum and difference with 3 values
- Thread starter afrocod
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- Difference Sine Sum
In summary, the conversation discussed the formulas for calculating the sine of the sum and difference of three values, how these formulas can be simplified using trigonometric identities, their relationship as complementary functions, and their applications in real life.
sin (90 - θ + λ)
= sin90cos(θ + λ) - cos90sin(θ + λ)
= cos(θ + λ)
The book says cos(θ - λ)
So are we both right and if so how can I manipulate mine to look like the books answer.
- #2
tiny-tim
Science Advisor
Homework Helper
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hi afrocod! 
no, sin (90 - θ + λ) = sin (90 - (θ - λ))
= sin90cos(θ - λ) - cos90sin(θ - λ)
afrocod said:
no, sin (90 - θ + λ) = sin (90 - (θ - λ))
= sin90cos(θ - λ) - cos90sin(θ - λ)
- #3
afrocod
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Ah my old friend Tim.
I was surprised that 100's of people looked at this and nobody answered. I suspected this was a super easy question, as you just proved.
Thank you very much.
I was surprised that 100's of people looked at this and nobody answered. I suspected this was a super easy question, as you just proved.
Thank you very much.
1. What is the formula for calculating the sine of the sum of three values?
The formula for calculating the sine of the sum of three values is sin(A + B + C) = sin(A)cos(B)cos(C) + cos(A)sin(B)cos(C) + cos(A)cos(B)sin(C) - sin(A)sin(B)sin(C), where A, B, and C are the three given values.
2. How do you calculate the sine of the difference of three values?
The formula for calculating the sine of the difference of three values is sin(A - B - C) = sin(A)cos(B)cos(C) - cos(A)sin(B)cos(C) - cos(A)cos(B)sin(C) + sin(A)sin(B)sin(C), where A, B, and C are the three given values.
3. Can the sine of sum and difference with three values be simplified?
Yes, the sine of sum and difference formulas can be simplified using the trigonometric identities of double angle and half angle. However, the final answer will depend on the values of A, B, and C, and may not always be simplified.
4. What is the relationship between the sine of sum and difference with three values?
The relationship between the sine of sum and difference with three values is that they are complementary functions. This means that the sine of the sum of two angles is equal to the cosine of the difference of the same two angles, and vice versa.
5. How is the sine of sum and difference with three values used in real life?
The sine of sum and difference with three values is used in many fields such as physics, engineering, and astronomy. It is used to calculate the amplitude and phase shift of wave functions, as well as to analyze the interference patterns of waves. It is also used in navigation and GPS systems to determine the position of objects relative to each other.
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