anonymous
  • anonymous
If sin(theta)=X, then express sec(theta) in terms of x
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
The answer I got was \[\sqrt{1-(1/x)^2}\] Would this be correct?
freckles
  • freckles
|dw:1438813890812:dw| use pythagorean theorem to find the other side
freckles
  • freckles
and recall for secant use hyp/adj

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
I'm sorry, I'm a bit confused where to go from there
freckles
  • freckles
can you find the adjacent side by use of Pythagorean theorem ?
freckles
  • freckles
\[(\text{ adjacent })^2+x^2=1^2 \\ \text{ solve for adjacent }\]
freckles
  • freckles
let me know if you don't know how maybe I can give you a step
anonymous
  • anonymous
adjacent= -x+1?
freckles
  • freckles
\[( \text{ adjacent } )^2+x^2=1 \\ \text{ subtract} x^2 \text{ on both sides } \\ ( \text{ adjacent })^2=1-x^2 \\ \text{ take square root of both sides } \\ \text{ adjacent } = \pm \sqrt{1-x^2}\] you cannot simplify this ... if that is what you tried to do
freckles
  • freckles
|dw:1438814521770:dw| now find sec(theta) using the right triangle
anonymous
  • anonymous
The whole negative thing kinda threw me off. Thanks
anonymous
  • anonymous
What I tried to do initially was rewrite the identity sin^2+Cos^2=1 and go from there
freckles
  • freckles
you can use that too
freckles
  • freckles
\[\sin^2(\theta)+\cos^2(\theta)=1 \\ \text{ we are given } \sin(\theta)=x \text{ so } \sin^2(\theta)=x^2 \\ x^2+\cos^2(\theta)=1 \\ \\ \text{ subtract} x^2 \text{ on both sides } \\ \cos^2(\theta)=1-x^2 \\ \text{ take square root of both sides } \\ \cos(\theta)=\pm \sqrt{1-x^2}\] then just flip both sides to find sec(theta)
freckles
  • freckles
its the same thing really
anonymous
  • anonymous
Ooh, I tried to use the recirpocals first, hence why I had (1/x)^2 Thanks a bunch mate (:
freckles
  • freckles
np
freckles
  • freckles
well csc^2(x) would actually be (1/x)^2
anonymous
  • anonymous
Yeah, I figured if the identity works with sin and cos, it'd work with their reciprocals. I see the error
anonymous
  • anonymous
Do you think you might be able to help me with one more question?
freckles
  • freckles
i can try
anonymous
  • anonymous
Evaluate cos1+cos2+cos3+...+cos357+cos358+cos359 (all measurements are in degrees) The only thing I can imagine is that it repeats at a certain point or something
freckles
  • freckles
\[\cos(x)+\cos(180-x) \\=\cos(x)+\cos(180)\cos(x)-\sin(180)\sin(x) \\ =\cos(x)-1\cos(x)-0\sin(x)\\ =0\] So I think maybe we can use cos(x)+cos(180-x)
freckles
  • freckles
So I think maybe we can use cos(x)+cos(180-x)=0*
freckles
  • freckles
\[\cos(1)+\cos(179)=0 \\ \cos(2)+\cos(178)=0 \\ \cos(3)+\cos(177)=0 \\ \cos(4)+\cos(176) =0 \\ \cdots \\ \] and I have to come back to finish this i'm being called away unfortunately
anonymous
  • anonymous
Alright
freckles
  • freckles
notice above I put a minus but it doesn't matter that one part is still 0 \[\cos(x)+\cos(180-x) \\=\cos(x)+\cos(180)\cos(x)+\sin(180)\sin(x) \\ =\cos(x)-1\cos(x)+0\sin(x)\\ =0\] hmm... \[\cos(180)=-1 \\ \text{ hmmm... we need to think now for the rest of the finite series }\] like we already know cos(1)+cos(2)+...+cos(180)=-1 we need to figure out would to do with cos(181)+cos(182)+cos(183)+...+cos(359) we should be able to think of something similar
freckles
  • freckles
how about for that other sign try to see if something like cos(180+x)+cos(360-x)=0 works.. cos(180)cos(x)-sin(180)sin(x)+cos(360)cos(x)+sin(360)sin(x) =-cos(x)+cos(x)=0

Looking for something else?

Not the answer you are looking for? Search for more explanations.