Simplifying Core 3 Compound Angles: A Guide

In summary, The conversation is about simplifying cosBcosB + sinBsinB, which is equal to 1 according to the answer in the book. The discussion then moves to defining cosine and sine in terms of right-angled triangles or using SOHCAHTOA. The conversation also mentions the interpretation of sine and cosine when the hypotenuse equals 1 and how it relates to the Pythagorean theorem.
  • #1
CathyLou
173
1
Hi.

Could someone please tell me the method to use to simplify cosBcosB + sinBsinB?

Any help would be really appreciated.

Thank you.

Cathy
 
Last edited:
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  • #2
Well, isn't that equal to 1??
 
  • #3
arildno said:
Well, isn't that equal to 1??

Yeah, 1 is the answer in the back of the book. I just do not know why. Could you please explain?

Thank you.

Cathy
 
  • #4
Well, how was cosine and sine to an angle defined to you in the first place?

Perhaps in terms of right-angled triangles?
 
  • #5
arildno said:
Well, how was cosine and sine to an angle defined to you in the first place?

Perhaps in terms of right-angled triangles?

Do you mean by using SOHCAHTOA?
 
  • #6
Since I'm not English, I don't know what SOHCAHTOA means.

I assume it is related to:
[tex]\cos(v)=\frac{adjacentside}{hypotenuse},\sin(v)=\frac{oppositeside}{hypotenuse}[/tex]

Now, what interpretation of sine and cosine do you get if the hypotenuse equals 1?
(Alternatively, you may have learned about how sine and cosine are defined on the unit circle).


In this case, with the hypotenuse equal to 1, what do we get out of the Pythagorean theorem?
 

1. What are "Core 3 Compound Angles"?

"Core 3 Compound Angles" refer to a set of mathematical concepts and formulas used to solve problems involving three-dimensional objects and their angles.

2. Why are "Core 3 Compound Angles" important in science?

Understanding "Core 3 Compound Angles" is crucial in fields such as physics, engineering, and architecture, as it allows for accurate measurements and calculations of angles in three-dimensional space.

3. What are some real-life applications of "Core 3 Compound Angles"?

"Core 3 Compound Angles" are used in a variety of real-world scenarios, including designing buildings and structures, calculating trajectories in physics, and determining the angles of joints in robotics.

4. How do you calculate "Core 3 Compound Angles"?

The calculation of "Core 3 Compound Angles" involves using trigonometric functions such as sine, cosine, and tangent, as well as the Pythagorean theorem and other geometric principles.

5. Are there any common mistakes when working with "Core 3 Compound Angles"?

Some common mistakes when dealing with "Core 3 Compound Angles" include forgetting to convert between degrees and radians, mixing up trigonometric functions, and using the wrong formula for a specific scenario. It is essential to double-check all calculations and formulas to avoid errors.

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