Why does sin80°csc80° equal 1?

[CrossFit415]

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

 

[CrossFit415]

And I also have trouble doing this...

Cos400° • sec40°= 1 I don't understand how they got one.

 

[Mark44]

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?

 

[Mark44]

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?

 

[CrossFit415]

Replace csc80° with 1/sin? U

 

[Mark44]

Replace csc80° with 1/sin? U

No - replace csc80° with 1/sin80°.

 

[Mentallic]

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

 

[CrossFit415]

Thanks a lot for the help!

 

[CrossFit415]

As far as the cosine is concerned, 400° is the same as what standard angle?

Same angle as 40°

 

[HallsofIvy]

Yes, so cos(400)= cos(40). Now, what is sec(40) equal to?

 

[CrossFit415]

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.