Trig - Double Angles Questions,

In summary, the conversation is about double angle identities in trigonometry. The correct identities are given as sin2x = 2sinxcosx and cos2x = cos^2x - sin^2x = 2sin^2x - 1 = 2cos^2x - 1. The person who asked for help initially had incorrect identities but later corrected them. Another person points out that the signs are off in the corrected identities.
  • #1
Macleef
30
0
Trig - Double Angles Questions, Please Help!

please close, solved all my problems myself...
 
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  • #2
Double Angle Identities are as follows:
sin2x = 2sinxcosx

cos2x = cos^2x - sin^2x
= 2sin^2x - 1
= 2cos^2x - 1
first off, your double-angle identities are wrong

[tex]\cos{2x}=\cos^{2}x-\sin^{2}x[/tex]

[tex]\cos{2x}=2\cos^{2}x-1[/tex]

[tex]\cos{2x}=1-2\sin^{2}x[/tex]
 
  • #3
rocophysics said:
first off, your double-angle identities are wrong

[tex]\cos{2x}=\cos^{2}x-\sin^{2}x[/tex]

[tex]\cos{2x}=2\cos^{2}x-1[/tex]

[tex]\cos{2x}=1-2\sin^{2}x[/tex]

what are you talking about? they're exactly the same
 
  • #4
Macleef said:
what are you talking about? they're exactly the same
your signs are off, i haven't checked your work though
 

1. What are double angles in trigonometry?

Double angles in trigonometry refer to angles that are twice the size of a given angle. This can be expressed through formulas such as sin(2x) = 2sin(x)cos(x) and cos(2x) = cos^2(x) - sin^2(x).

2. How do you find the double angle of a given angle?

To find the double angle of a given angle, you can use the formulas sin(2x) = 2sin(x)cos(x) and cos(2x) = cos^2(x) - sin^2(x). Alternatively, you can also use the half-angle identities, such as sin(x/2) = ±√[(1-cos(x))/2] and cos(x/2) = ±√[(1+cos(x))/2].

3. What is the purpose of using double angles in trigonometry?

Double angles are useful in simplifying trigonometric expressions and solving trigonometric equations. They can also be used to find the values of trigonometric functions for larger angles by using the values for smaller angles.

4. How are double angles used in real-world applications?

Double angles are used in various fields such as engineering, physics, and astronomy. They can be used to calculate distances, angles, and forces in real-world problems involving triangles and circular motion.

5. Are there any other types of multiple angles besides double angles?

Yes, there are triple angles and half angles. Triple angles are three times the size of a given angle and can be expressed through formulas such as sin(3x) = 3sin(x) - 4sin^3(x) and cos(3x) = 4cos^3(x) - 3cos(x). Half angles, as mentioned earlier, are half the size of a given angle and can be expressed through the half-angle identities.

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