How to Find Cosine from Secant Using Trig Identities?

In summary, the problem asks to find the value of $\sec(\pi-\pi/3)$ given that $\cos(\pi/3)=1/2$. The identity to use is the definition of secant as the reciprocal of cosine. To get cosine from secant, we take the reciprocal of both sides of the equation.
  • #1
courtbits
15
0
If \(\displaystyle \cos(\pi/3)= \frac{1}{2}\), find \(\displaystyle \sec(\pi-\pi/3)\)

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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  • #2
courtbits said:
If \(\displaystyle \cos(\pi/3)= \frac{1}{2}\), find \(\displaystyle \sec(\pi-\pi/3)\)

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...

$\displaystyle \begin{align*} \frac{1}{\cos{(x)}} \equiv \sec{(x)} \end{align*}$
 
  • #3
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..
 

FAQ: How to Find Cosine from Secant Using Trig Identities?

What are trig identities and why are they important?

Trig identities are mathematical equations involving trigonometric functions that are used to simplify and solve complex problems. They are important because they allow us to manipulate and transform trigonometric expressions into simpler forms, making it easier to solve problems in mathematics, physics, and engineering.

What are the basic trig identities?

The basic trig identities include the Pythagorean identities, reciprocal identities, quotient identities, and negative angle identities. These identities are used to relate the six trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) to each other and to find values of trigonometric functions for different angles.

How can I prove trig identities?

There are several methods to prove trig identities, including using algebraic manipulation, using basic trigonometric identities, using the unit circle, and using special triangles. It is important to remember that when proving an identity, you must start with one side of the equation and manipulate it until it is equal to the other side.

What are some common mistakes when solving trig identities?

Some common mistakes when solving trig identities include forgetting to distribute negative signs, making algebraic errors, not simplifying expressions fully, and using incorrect identities. It is important to double check your work and use multiple methods to verify the solution.

How can I improve my understanding of trig identities?

To improve your understanding of trig identities, it is important to practice solving problems and familiarize yourself with the different identities. You can also use visual aids, such as the unit circle, to help you visualize the relationships between the trigonometric functions. Additionally, seeking help from a tutor or participating in a study group can also be beneficial.

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