I would certainly like to recognize if there is a basic technique to fix equation looking choose this:

$$ an(sec^-1 4)$$

without making use of a calculator (you need to discover the precise value)?

How to proceed?


*

*

Imagine a right-angled triangle through one leg $k$ and hypotenuse $4k$ and angle $ heta$ in between them. Then $cos heta = frack4k= frac14$ and $sec heta = 4$, making $sec^-14 = heta$.

The opposite leg is $sqrt(4k)^2-k^2=sqrt15k$ and so $ an(sec^-14) = an heta = fracsqrt15kk=sqrt15$. Now you might need a calculator.

You are watching: Sec^-1(4)


*

Let $sec^-14= hetaimpliessec heta=4$

Now, $ an^2 heta=sec^2 heta-1$

Finally utilizing the definition of the primary value of $sec^-1,00$


*

Thanks for contributing a solution to steustatiushistory.orgematics Stack Exchange!

Please be certain to answer the question. Provide details and share your research!

But avoid

Asking for assist, clarification, or responding to various other answers.Making statements based on opinion; ago them up through recommendations or individual experience.

Use steustatiushistory.orgJax to format equations. steustatiushistory.orgJax reference.

See more: Meaning Of Put The Fear Of God In Them ' Mean? Put The Fear Of God Into Somebody

To learn even more, check out our tips on writing great answers.


Post Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy plan and cookie policy


Not the answer you're looking for? Browse other inquiries tagged trigonomeattempt or ask your own question.


If $2 an^2 x - 5sec x - 1 = 0$ has 7 roots in $< 0,fracnpi2>$ then the biggest worth of $n$ is?
Solving the value of $x$ for the equation $frac (sec x + an x)^2 - (sec 2x + an x)^2sin 2x - sin x = 2$
*

website architecture / logo design © 2021 Stack Exreadjust Inc; user contributions licensed under cc by-sa. rev2021.9.28.40331


Your privacy

By clicking “Accept all cookies”, you agree Stack Exreadjust have the right to keep cookies on your tool and discshed indevelopment in accordance with our Cookie Policy.