INPUT ARTICLE: Article: The terms "sine," "cosine," and "tangent" all refer to various ratios between the angles and/or sides of a right triangle.  In a right triangle, the sine of an angle is defined as the length of the side opposite the angle divided by the hypotenuse of the triangle.  The abbreviation for sine found in equations and on calculators is sin. Even a basic scientific calculator will have a sine function.  Look for a key marked sin.  To find the sine of angle, you will usually press the sin key and then enter the angle measurement in degrees.  On some calculators, however, you must enter the degree measurement first and then the sin key.  You will have to experiment with your calculator or check the manual to find out which it is.  To find the sine of an 80 degree angle, you will either need to key in sin 80 followed by the equal sign or enter key, or 80 sin. (The answer is -0.9939.) You can also type in "sine calculator" into a web search, and find a number of easy-to-use calculators that will remove any guesswork. The Law of Sines is a useful tool for solving triangles.  In particular, it can help you find the hypotenuse of a right triangle if you know the length of one side, and the measure of one other angle in addition to the right angle.  For any triangle with sides a, b, and c, and angles A, B, and C, the Law of Sines states that a / sin A = b / sin B = c / sin C. The Law of Sines can actually be used to solve any triangle, but only a right triangle will have a hypotenuse. The hypotenuse (longest side) must be "c".  For the sake of simplicity, label the side with the known length as "a," and the other "b".  Then assign variables A, B, and C to the angles of the triangle.  The right angle opposite the hypotenuse will be "C".  The angle opposite side "a" is angle "A," and the angle opposite side "b" is "B". Because it is a right angle, you already know that C = 90 degrees, and you also know the measure of A or B.  Since the internal degree measurement of a triangle must always equal 180 degrees, you can easily calculate the measurement of the third angle using the following formula: 180 – (90 + A) = B.  You can also reverse the equation such that 180 – (90 + B) = A. For example, if you know that A = 40 degrees, then B = 180 – (90 + 40). Simplify this to B = 180 – 130, and you can quickly determine that B = 50 degrees. At this point, you should know the degree measurements of all three angles, and the length of side a.  It is now time to plug this information into the Law of Sines equation to determine the lengths of the other two sides. To continue our example, let's say that the length of side a = 10.  Angle C = 90 degrees, angle A = 40 degrees, and angle B = 50 degrees. We just need to plug our numbers in and solve the following equation to determine the length of hypotenuse c: length of side a / sin A = length of side c / sin C.  This might still look a bit intimidating, but the sine of 90 degrees is a constant, and always equals 1!  Our equation can thus be simplified to: a / sin A = c / 1, or just a / sin A = c. You can do this in two separate steps, by first calculating sin A and writing it down, and then dividing by a.  Or you can key it all into the calculator at the same time.  If you do, remember to include parentheses after the division sign.  For example, key in either 10 / (sin 40) or 10 / (40 sin), depending on your calculator. Using our example, we find that sin 40 = 0.64278761.  To find the value of c, we simply divide the length of a by this number, and learn that 10 / 0.64278761 = 15.6, the length of our hypotenuse!

SUMMARY: Understand what "Sine" means. Learn to calculate sine. Learn the Law of Sines. Assign the variables a, b, and c to the sides of your triangle. Calculate the measurement of the third angle. Examine your triangle. Apply the Law of Sines to your triangle. Divide the length of side a by the sine of angle A to find the length of the hypotenuse!

INPUT ARTICLE: Article: Use a spice grinder to grind the toasted sesame seeds into a fine powder. There should be no solid seeds left when done. If you do not have a spice grinder, consider using a coffee grinder or mortal and pestle, instead. In a small bowl, whisk together the ground sesame seeds, dashi, soy sauce, sugar, sake, rice vinegar, and black pepper until the mixture is evenly blended.  For this sauce, you could pulse the ingredients together using a blender instead of whisking by hand, if desired. Doing so can help combine the solid ingredients—the ground sesame seeds, the sugar, and the black pepper—more thoroughly. Note that this is the other common sauce served with shabu shabu, and it, too, can be purchased commercially to save time. This sauce will end up being light brown. Transfer the sauce to a second shallow serving dish.  The bowl needs to be shallow so that you can dip food into the sauce without difficulty. Do not combine the sesame sauce and ponzu sauce. The two must be kept in separate dishes. The sauce can be served without any garnishes, but garnishes can add color and an extra splash of taste. Thinly sliced green onions, a small sprinkle of chopped garlic, and a dash of ground red pepper are good choices for sesame sauce.  Add the garnishes to taste. Keep in mind that they should accent the sauce, not overwhelm it or mask it. Set the sesame sauce aside until you are ready to serve the shabu shabu.

SUMMARY:
Grind the sesame seeds into a powder. Combine the sauce ingredients. Pour into a serving dish. Add the garnishes, if desired.