Find the trigonometric ratios indicated

Otis

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but why am i not wrong with the sec…
i did not put Sec0 =z/e
I'm not sure that I understand.

You did write sec(θ) = z/e

huh.JPG

With the corrected labels, you have:

cos(θ) = ω/Z

sec(θ) = Z/ω

ω/Z and Z/ω are reciprocals, so you have sec(θ) = 1/cos(θ).

:)
 

ugudansam

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Nov 23, 2021
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If they are reciprocals, do it mean that w/z cancels z/w ? If yes, why cant we also say cos(0) = 1/Sec(0) ? I used 0 to represent tita
 

ugudansam

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Here is my final solution. I hope i am correct? Thanks for your teaching
 

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Otis

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I hope i am correct?
Hi ugudansam. All answers look correct!

Two comments. Some letters 'a' look like '9'. You may want to be mindful of that. On #3, you'd written the answer for sec(β) twice. (No big deal.)

onp.JPG

Cheers :)
 

Otis

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If they are reciprocals, [doesd] it mean that w/z cancels z/w ?
No. It means that you may write each as the reciprocal of the other.

If we multiply two reciprocals, we get 1. (Maybe that's what you meant by w/Z cancelling Z/w.)

You have correctly shown the identities:

sec(θ) = 1/cos(θ)

1/sec(θ) = cos(θ)

😎
 

ugudansam

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Nov 23, 2021
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Hi ugudansam. All answers look correct!

Two comments. Some letters 'a' look like '9'. You may want to be mindful of that. On #3, you'd written the answer for sec(β) twice. (No big deal.)

View attachment 29888

Cheers :)
So grateful, and yes, I wrote the answer twice since the question came twice. Thanks for the tutorial as I will further the study here. However, for the formula or secant, cosecant and cotangent. I hear something like (ALL STUDENT LIKE CHEMISTRY) I wonder the application. Else it mean one just have to memorise them
 

Otis

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Apr 22, 2015
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I wrote the answer twice since the question came twice.
Indeed it does. Good on ya.

formula for secant, cosecant and cotangent ... [maybe] one just have to memorise them
Or, one could memorize cosine, sine, and tangent definitions, first. That way, you simply write their reciprocals, to get the other three. You'd only need to remember that the name secant is associated with cosine and the name cosecant is associated with sine.

When I was a beginner, I think I'd linked secant and cosine together because both names have two syllables, and that helped me remember that secant is the reciprocal of cosine.

:)
 
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