Why does sin80°csc80° equal 1?

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Homework Help Overview

The discussion revolves around trigonometric identities, specifically examining why the expression sin(80°) * csc(80°) equals 1, as well as exploring the relationship between cos(400°) and sec(40°).

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are questioning the multiplication involved in the expression sin(80°) * csc(80°) and how it simplifies to 1. There is also inquiry into the equivalence of cos(400°) and sec(40°) and how they relate to standard angles.

Discussion Status

Some participants have provided guidance on replacing csc(80°) with 1/sin(80°) and have pointed out the relationship between angles, suggesting that cos(400°) is equivalent to cos(40°). There is an ongoing exploration of these identities without a clear consensus yet.

Contextual Notes

Participants are working under constraints such as the use of mobile devices, which may limit their ability to use standard mathematical symbols. There is also an emphasis on understanding rather than simply stating results.

CrossFit415
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I'm on mobile so I can't use regular symbols.

Sin80°csc80° = 1 why does this equal one? Is there multiplication involved here?

I know csc = 1/sin
 
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And I also have trouble doing this...

Cos400° • sec40°= 1 I don't understand how they got one.
 
CrossFit415 said:
I'm on mobile so I can't use regular symbols.

Sin80°csc80° = 1 why does this equal one? Is there multiplication involved here?

I know csc = 1/sin
More precisely, csc(x) = 1/sin(x), so what can you replace csc(80°) by?
 
CrossFit415 said:
And I also have trouble doing this...

Cos400° • sec40°= 1 I don't understand how they got one.
As far as the cosine is concerned, 400° is the same as what standard angle?
 
Replace csc80° with 1/sin? U
 
CrossFit415 said:
Replace csc80° with 1/sin? U
No - replace csc80° with 1/sin80°.
 
CrossFit415 said:
I'm on mobile so I can't use regular symbols.

Sin80°csc80° = 1 why does this equal one? Is there multiplication involved here?

I know csc = 1/sin

Yes, so what is [tex]sin(80^o)\cdot\frac{1}{sin(80^o)}[/tex] ?
 
Thanks a lot for the help!
 
Mark44 said:
As far as the cosine is concerned, 400° is the same as what standard angle?

Same angle as 40°
 
  • #10
Yes, so cos(400)= cos(40). Now, what is sec(40) equal to?
 
  • #11
HallsofIvy said:
Yes, so cos(400)= cos(40). Now, what is sec(40) equal to?

Cos is the same angle as 40° . sec = 1/cos40° and they cancel out to be 1.
 

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