Vertices because those are a little bit easier to think about. To this point over here, and I'm just picking the I've now rotated it 90 degrees, so this point has now mapped Points I've now shifted it relative to that point So, every point that was on the original or in the original set of So I could rotate it, I could rotate it like, that looks pretty close to a 90-degree rotation. So if I start like this IĬould rotate it 90 degrees, I could rotate 90 degrees, Rotate it around the point D, so this is what I started with, if I, let me see if I can do this, I could rotate it like,Īctually let me see. I have another set of points here that's represented by quadrilateral, I guess we could call it CD orīCDE, and I could rotate it, and I rotate it I would In fact, there is an unlimited variation, there's an unlimited numberĭifferent transformations. That is a translation,īut you could imagine a translation is not the If I put it here every point has shifted to the right one and up one, they've all shifted by the same amount in the same directions. In the same direction by the same amount, that's Shifted to the right by two, every point has shifted This one has shifted to the right by two, this point right over here has Just the orange points has shifted to the right by two. Onto one of the vertices, and notice I've now shifted Let's translate, let's translate this, and I can do it by grabbing That same direction, and I'm using the Khan Academy To show you is a translation, which just means moving all the points in the same direction, and the same amount in Transformation to this, and the first one I'm going This right over here, the point X equals 0, y equals negative four, this is a point on the quadrilateral. You could argue there's an infinite, or there are an infinite number of points along this quadrilateral. Of the quadrilateral, but all the points along the sides too. Not just the four points that represent the vertices For example, this right over here, this is a quadrilateral we've plotted it on the coordinate plane. It's talking about taking a set of coordinates or a set of points, and then changing themĭifferent set of points. You're taking something mathematical and you're changing it into something else mathematical, In a mathematical context? Well, it could mean that Something is changing, it's transforming from Transformation in mathematics, and you're probably used to (geometric progress).Introduce you to in this video is the notion of a If the csc of an angle complementary to A be \(\frac\) are in G.P. Solved Examples on Trigonometrical Ratios Table:ġ. The cotangent of the standard angles 0°, 30°, 45°, 60° and 90°: The secant of the standard angles 0°, 30°, 45°, 60° and 90°: The cosine of the standard angles 0°, 30°, 45°, 60° and 90°: The tangent of the standard angles 0°, 30°, 45°, 60° and 90°: Values of the other trigonometrical ratios of the standard angles. Standard angles from the trigonometrical ratios table therefore we can easily find the Since, we know the sin and cos value of the Respectively the positive square roots of 4/4, 3/4, 2/4, 1/4, 0/4 Similarly cosine of the above standard angels are The standard angles 0°, 30°, 45°, 60° and 90° are respectively the If θ be an acute angle, the values of sin θ and cos θ lies between 0 and 1 (both inclusive). (d) write the values of sin 0°, sin 30°, sin 45°, sin 60° and sin 90° in reverse order and get the values of cos 0°, cos 30°, cos 45°, cos 60° and cos 90° respectively. (c) these numbers given the values of sin 0°, sin 30°, sin 45°, sin 60° and sin 90° respectively. (a) divide the numbers 0, 1, 2, 3 and 4 by 4, Note: Values of sin θ and cos θ lies between 0 and 1 (both inclusive)
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