Why does sin80°csc80° equal 1?

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SUMMARY

The equation sin(80°) * csc(80°) equals 1 due to the definition of the cosecant function, where csc(80°) is the reciprocal of sin(80°). Therefore, sin(80°) * (1/sin(80°)) simplifies directly to 1. Additionally, the expression cos(400°) * sec(40°) also equals 1, as cos(400°) is equivalent to cos(40°), and sec(40°) is defined as 1/cos(40°), leading to the same cancellation effect.

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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 sin(80^o)\cdot\frac{1}{sin(80^o)} ?
 
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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