Prove another Trigonometric Function

In summary: You could try substituting sin^2 for cos^2 in the last two equations.That might work. But I'm not sure. I'm still having trouble with that last equation.In summary, the student is having difficulty solving trigonometric equations and is seeking help.
  • #1
Sabellic
68
0

Homework Statement



http://img362.imageshack.us/img362/1465/problemcn2.jpg [Broken]
http://g.imageshack.us/g.php?h=362&i=problemcn2.jpg [Broken]

Homework Equations


http://img510.imageshack.us/img510/3137/formula1df4.jpg [Broken]
http://g.imageshack.us/g.php?h=510&i=formula1df4.jpg [Broken]

http://img411.imageshack.us/img411/7889/formula2mn1.jpg [Broken]
http://g.imageshack.us/g.php?h=411&i=formula2mn1.jpg [Broken]


The Attempt at a Solution



http://img380.imageshack.us/img380/5177/attemptsu1.jpg [Broken]
http://g.imageshack.us/g.php?h=380&i=attemptsu1.jpg [Broken]

As you can see, none of my calculations match. Please help anyone. I know this is very difficult to explain but I'm all ears. This question's been bothering me all afternoon. The curriculum does not explain it well. At all.

Mega thanks in advance.
 
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  • #2
You got the formulas for cos(X+B) and cos(X-B) wrong.
 
  • #4
Oh, damn am I stupid. Thanks for telling me about the mistake.

Alright guys, I got the first 2 parts correct so far (because of the correct Cos addition identity). Now on to the next two. I'm not out of the woods yet.
 
  • #6
Look at your list of trig identities. Which ones involve cos^2 and/or sin^2?
 
  • #8
Ok, so you know 1. [itex]\sin^2 \theta = 1 - \cos^2 \theta [/itex] 2. [itex]\cos^2 \theta = 1 - \sin^2 \theta [/itex]. With your cos^2 - sin^2 form, replace the appropriate terms.
 
  • #9
Ok. I tried doing that but it just brought me back to the original equation.

http://img244.imageshack.us/img244/7475/pict0139ko2.jpg [Broken]
http://g.imageshack.us/g.php?h=244&i=pict0139ko2.jpg [Broken]

As well, I don't know how to apply the First Pythagorean Identity to sin or cos if it is multiplied by 2. It changes things. And they never went over how to mechanically solve these operations in my curriculum.
 
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  • #11
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1. What are the other trigonometric functions besides sine, cosine, and tangent?

There are three other commonly used trigonometric functions: secant, cosecant, and cotangent. These functions are defined as the reciprocal of cosine, sine, and tangent, respectively.

2. How do you prove the values of these trigonometric functions?

The values of these functions can be proved using the unit circle, which relates the trigonometric functions to the coordinates of a point on a circle with a radius of 1 unit. Alternatively, their values can also be derived using trigonometric identities or by using a scientific calculator.

3. What is the importance of proving trigonometric functions?

Proving trigonometric functions allows us to understand the relationships between different angles and sides in a right triangle. It also helps in solving complex mathematical problems involving trigonometric functions, such as in geometry, physics, and engineering.

4. Can you prove trigonometric functions for angles beyond 90 degrees?

Yes, the trigonometric functions can be extended to angles beyond 90 degrees using the unit circle or by using the concept of reference angles. These extended functions are known as inverse trigonometric functions.

5. Are there any real-world applications of proving trigonometric functions?

Yes, trigonometric functions are widely used in various fields such as navigation, surveying, astronomy, and architecture. They are also used in the development of computer graphics and animation, as well as in the study of waves and vibrations in physics and engineering.

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