MHB How to Find Cosine from Secant Using Trig Identities?

AI Thread Summary
To find secant from cosine, recall that secant is defined as the reciprocal of cosine, meaning sec(x) = 1/cos(x). For the angle π - π/3, which simplifies to 2π/3, the cosine value can be determined using the cosine identity for supplementary angles: cos(π - x) = -cos(x). Given that cos(π/3) = 1/2, it follows that cos(2π/3) = -1/2. Therefore, sec(2π/3) = 1/cos(2π/3) = -2. This illustrates the relationship between cosine and secant through trigonometric identities.
courtbits
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If $$\cos(\pi/3)= \frac{1}{2}$$, find $$\sec(\pi-\pi/3)$$

Someone really give me step-by-step explanation.
I really don't know what identity to use, and no idea how to get cosine to secant.
Please, it would help. I do have more questions if you help me dissect this problem. XD
Thanks so much in advance!
 
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courtbits said:
If $$\cos(\pi/3)= \frac{1}{2}$$, find $$\sec(\pi-\pi/3)$$

Someone really give me step-by-step explanation.
I really don't know what identity to use, and no idea how to get cosine to secant.
Please, it would help. I do have more questions if you help me dissect this problem. XD
Thanks so much in advance!

No idea how to get cosine from secant? By DEFINITION the secant is the reciprocal of the cosine...

$\displaystyle \begin{align*} \frac{1}{\cos{(x)}} \equiv \sec{(x)} \end{align*}$
 
Prove It said:
No idea how to get cosine from secant? By DEFINITION the secant is the reciprocal of the cosine...

$\displaystyle \begin{align*} \frac{1}{\cos{(x)}} \equiv \sec{(x)} \end{align*}$

Ok..
 

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