What is the tangent of a line?
I will attempt to answer this question as a mom would attempt to explain it to her 16 year old high school student daughter because I had to help her understand that this year. I'm not math wiz with all the graphics and fancy explanations so please just take it as a simple answer.When my daughter asked me what Tangent (or Tan) is, I explained it's link with Sine and Cosine... The sine and cosine are represented on a line and look like waves. The are curbed lines. You were asking is the tangent line was in reference to a curbed or straight line and this sine / cosine curbed aspect is important for my answer.So, sine and cosine are curbed. Visualise that the "wave" of these is like half circles linked together. When I explained it to my daughter, I put three CDs next to each other and touching each other on a table. I said, sine and cosine will show a curb that looks like this... and I started at the left (first CD) went down the curb of the bottom half of the first CD, continued going in a curb up the top half of the second CD and then down again on the curb of the third CD.I then told her... with a square, it's easy to see in what direction the line is going because you have straight lines so you can derive the slope of any of the sides by using two points in a Cartesian plane (because she was working with that method at the moment for straight lines). But with a circle, it's hard to know how "curby" the curb of the circle is. Tangent helps to figure that part out.With a circle or other curbs... to find out how "curby" the curb is, you kind of have to use lines too. That line is called Tangent (Tan). I then I showed her visually how to observe tangent with the example with the CD.I put a ruler against the first CD and said... "like this". A circle is like a line that changes direction at every infinitely small point on it's line. At each point, the slope of that ruler kind of changes ever so slightly. When it is at the top or at the bottom of the circle... it is horizontal. When it is at the leftest or rightest end of the circle, it is vertical... but between these positions, the slope of the line changes at every point.Knowing the answer to tangent in relationship to the sine or cosine of "the wave" or curb will help you figure out how "curby" that curb is.My daughter "got it" by then so I hope you do too? That's my "mom's explanation" to "What is tangent?"
How do I find tan inverse of (0.05670)?
Hi there! Below is your answer,Use a log book (if you’re in school) or use a scientific calculator to find the valueHope this helps! Kindly revert back if any queries
Explain how to transform tan^(2)0 cos^(2)0 + cot^(2)0 sin^(2)0 into 1 ?
Do you mean this? tan²(0)cos²(0) + cot²(0)sin²(0) No, that is not 1. The expression cot²(0) is undefined, and that sinks the rest of the expression. Now it occurs to my that you might be using zero as a variable. Don't do that. Even if the zeros were replaced with variables, the expression would not be identically equal to 1. The identity would hold up only where all parts of the expression are real. tan²(θ)cos²(θ) + cot²(θ)sin²(θ) = 1, for θ ≠ kπ/2 for any integer k
What is the purpose of cos, tan, and sin in physics?
They are the basic trigonometric functions.They are derived from the following geometric relationship:Other algebraic functions can also be derived from this diagram…base of the natural log, e, pi and complex numbers/vectors.Then come calculus and differential equations…the mathematics of rate of change and the heart of general physics.It’s been said that all of physics is derived from the Pythagorean Theorem.
What am I doing wrong? Integrate tan^5x dx?
integrate tan^5x dx integral tan^4x tanx dx integral (sec^2x - 1)^2 tanx dx substitute u = secx | du = secxtanx dx | dx = du/secxtanx so integral (u^2 - 1)^2 tanx du/secxtanx integral (u^2-1)^2 du/secx integral (u^4-2u^2+1)du/u |since u = secx integral (u^3 -2u+1/u) du = u^4/4 - u^2 + ln|u| + C = (sec^4x)/4 - sec^2x + ln|secx| + C APPARENTLY the real answer is "(sec^4x)/4 - tan^2x + ln|secx| + C" according to the Book Why is this wrong and how come my method won't work
Indefinite intergral of tan 4x dx?
Well for tanx the integral is ln(secx) + C, so for tan4x it will be: ln(sec(4x)) / 4 + C Because if you derive ln(sec(4x)) you'll get 4*tan(4x).
Is "Thanks for the treat" correct?
More often you would not call it “the treat” but rather use the word treat to describe how you personally felt about their gift or kindness.Thank you! That was a real treat! Treat refers to it being a treat to you. Something out of the ordinary that brought you joy or happiness.A treat can also be a sweet or a candy, and then you likely would not refer to it as a treat except maybe on Halloween when people are saying “Trick or Treat”.Thanks for inviting me to dinner. It was a real treat! as I rarely get out for dinner. Much appreciated!I can’t believe you brought me chocolate all the way from Switzerland! What a treat!“treat” to me…how it made me feel…not the “thing” that you gave.