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Depending on which sides you have, you should choose sin, cos or tan, as shown in the diagram below. $$\begin{align} \sin d &= \frac{\text{opposite side}}{\text{hypoteneuse side}} \\ \cos d &= \frac{\text{adjacent side}}{\text{hypoteneuse side}} \\ \tan d &= \frac{\text{opposite side}}{\text{adjacent side}} \\ \end{align}$$
Mar 1, 2020 · Discover effective methods for remembering the exact values of sin, cos, & tan for common angles. This will be helpful for studying your maths GCSE.
- The Basic Two: Sine and Cosine
- The Other Four: Tangent, Cotangent, Secant, Cosecant
- Six Functions in One Picture
- Practice Problems
- BTW: Why Call It Sine?
A picture is worth a thousand words (which is why it takes a thousandtimes as long to download). The trig functions are nothing more thanlengths of various sides of a right triangle in various ratios.Since there are three sides, there are 3 × 2 = 6different ways to make a ratio (fraction) of sides. That’swhy there are six trig functions, no more an...
The other four functions have no real independent life of their own;they’re just combinations of the first two. You could do all oftrigonometry without ever knowing more than sines and cosines. But knowingsomething about the other four, especially the tangent, can often save you somesteps in a calculation—and your teacher will expect you to knowabo...
You saw earlierhow the sine and cosineof an angle are the sides of a triangle in a unit circle. It turns outthat all six functions can be shown geometrically in this way. In the illustration at right, triangle ABC has angle θ at thecenter of a unit circle (AB = radius = 1). You alreadyknow that BC = sin θ and AC = cos θ. What about tan θ? Well, sin...
To get the most benefit from these problems, work themwithout first looking at the solutions. Refer back to the chaptertext if you need to refresh your memory. Recommendation: Work them on paper —it’s harder to fool yourself about whether you reallyunderstand a problem completely. You’ll find fullsolutions for all problems. Don’t just check yourans...
From the picture, it’s obvious whythe name “tangent” makes sense: the tangent of an angle is the lengthof a segment tangent to the unit circle. But what about the sinefunction? How did it get its name? Please look at thepicture again, and notice thatsin θ= BC is half a chord of the circle.The Hindu mathematician Aryabhata the elder (about475–550) u...
How To Learn Trigonometry Intuitively – BetterExplained. Trig mnemonics like SOH-CAH-TOA focus on computations, not concepts: TOA explains the tangent about as well as x 2 + y 2 = r 2 describes a circle. Sure, if you’re a math robot, an equation is enough.
- Imagine Bob The Alien visits Earth to study our species.Without new words, humans are hard to describe: “There’s a sphere at the top, which gets sc...
- Nobody ever told me in my years of schooling: sine and cosine are percentages. They vary from +100% to 0 to -100%, or max positive to nothing to ma...
- Amazingly enough, your neighbor now decides to build a ceiling on top of your dome, far into the horizon. (What’s with this guy? Oh, the naked-man-...
- A short time ago I had zero “intuitive conclusions” about the cosecant. But with the dome/wall/ceiling metaphor, here’s what we see:Whoa, it’s the...
- Psst… don’t over-focus on a single diagram, thinking tangent is always smaller than 1. If we increase the angle, we reach the ceiling before the wa...
- For most of us, I’d say this is enough: 1. Trig explains the anatomy of “math-made” objects, such as circles and repeating cycles 2. The dome/wall/...
- You may see tangent defined as the length of the tangent line from the circle to the x-axis (geometry buffs can work this out).As expected, at the...
- Trig functions take an angle and return a percentage. sin(30) = .5 means a 30-degree angle is 50% of the max height.The inverse trig functions let...
- 1. How To Learn Trigonometry Intuitively 2. Easy Trig Identities With Euler's Formula 3. Intuition For The Law Of Cosines 4. Intuition For The Law...
Learn and revise trigonometric ratios of sine, cosine and tangent and calculate angles and lengths in right-angled triangles with GCSE Bitesize AQA Maths.
Try Sin Cos and Tan. Play with this for a while (move the mouse around) and get familiar with values of sine, cosine and tangent for different angles, such as 0°, 30°, 45°, 60° and 90°.
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Sine, Cosine and Tangent (often shortened to sin, cos and tan) are each a ratio of sides of a right angled triangle: For a given angle θ each ratio stays the same. no matter how big or small the triangle is. To calculate them: Divide the length of one side by another side. Example: What is the sine of 35°?
