Basically the title. I'm looking for a place to find all the trigonometric identities in one place. Including stuff like sin2A, 2sinAsinB, tan2A...literally everything. I've had enough with struggling to remember it, I'm going to memorize them once and for all, or at least bring my understanding to the point where I can derive any I don't know in an exam hall. But to do that I need all of them in one place. Please, someone?
i hate my class so much because there's 0 teaching; read a textbook, watch a 5-10 minute video then hopefully know everything.
- https://prnt.sc/20ds3jq
- https://prnt.sc/20ds49s
- https://prnt.sc/20ds4zl
- https://prnt.sc/20ds68q
- https://prnt.sc/20ds728
NOTE: This is not a last minute assignment I want anyone to complete, I just have NO IDEA HOW TO EVEN START TO SOLVE THESE QUESTIONS!!!!!! So even helping out in a question or two is appreciated. I literally am learning NOTHING.
Hello, how do I prove sinΒ²ΞΈsecΒ²ΞΈ= secΒ²ΞΈ - 1 ?
Attempt: https://imgur.com/a/nNSWxm8
I understood the Markscheme after realizing how they got the equation for x using the symmetry identities. But since cos( -A ) = cos( A ) shouldn't that mean I can take either A or -A in the final equation, why does only A end up giving me the correct equation for x? I might be doing something wrong here but this confused me.
Note ~ if my confusion here makes no sense I tried to make it clearer on the attempt
I am attempting to solve an equation of the following form for x:
A * cos-1(f(x)) + B * cos-1(g(x)) = C
where A, B, and C are constants. For my purposes, it is fine to fix A with a value of 2 and B with a small positive integer (say less than 10). C could be anything.
I know there is a trig identity for a inverse cosine addition but it doesn't include the constants A and B. I tried working through the proof for that identity but adding in the constants and got lost.
I also tried substituting the inverse cosines for their exponential equivalents, -i ln(x + sqrt(x2-1)). This seems like it has some potential but again I am lost.
Is there any hope to solve an equation of this form? If anyone is curious I can try to add some more context to the problem.
EDIT: A, B, and C are given. I'm looking for a solution in a form which lets me easily combine f(x) and g(x) through either addition/multiplication/etc
i was wondering if i can write all the trigonometric identities and ratios in the boards before starting the exam
The key to being able to rederive every formula by yourself is understanding. When you understand something you don't need to remember lots of detail but just the key ideas. When I was a TA in various universities I encountered many strong students that struggled with remembering trigonometric identities and how to derive the one they needed. They all complained that there are so many of them. Well here is a video that will teach you just that.
https://www.youtube.com/watch?v=sjNFRP25GvY&ab_channel=Math%2CPhysics%2CEngineeringAfter watching it I promise you will be able to rederive every identity yourself and will forever remember its proof.
so I have to establish the identity sec theta - cos theta = sin theta tan theta
starting from the left side I understand Sec theta can be rewritten as 1 / cos theta - cos theta = sin^2 theta / cos theta = sin theta * sin theta / cos theta
What I'm having trouble grasping is how 1 / cos theta - cos theta = sin^2 theta / cos theta
I feel like that is a pretty important concept to grasp and I just don't. Thanks for the help in advance.
also is there a better way to write theta short hand I feel like it gets wordy on here.
Image - https://imgur.com/a/okqpja8
How did they combine?
Did they add? I did add them and the "y" gets cancelled out by subtraction so..
Can anyone tell me how (2n+1)pi and (2npi) get combined to become npi? And also how the power of (-1) i.e., (2n+1) and (2n) combine to become n?
I don't understand the marked lines.. (Red dot and also highlighted in different color)
The key to being able to rederive every formula by yourself is understanding. When you understand something you don't need to remember lots of detail but just the key ideas. When I was a TA in various universities I encountered many strong students that struggled with remembering trigonometric identities and how to derive the one they needed. They all complained that there are so many of them. Well here is a video that will teach you just that.
https://studio.youtube.com/video/sjNFRP25GvY/analytics/tab-overview/period-default
After watching it I promise you will be able to rederive every identity yourself and will forever remember its proof.
