Use the knowledge of plane geometry to Express the sine through tothe sinus. According to the definition, the sineof the th angle in a right triangle is the ratio length opposite side to hypotenuse, andsineom – adjacent sides to the hypotenuse. Even the simple knowledge of the Pythagorean theorem will allow you in some cases to quickly find the desired transformation.
Express the sine through tothe sinus, using the elementary trigonometric identity, according to which the sum of the squares of these values gives one. Please note that correctly complete the task, you can only if you know in what quarter there is a specific angle, otherwise you will get two possible outcomes – positive and negative sign.
Remember the formula of the cast, which also allows to carry out the required operation. According to them, if the number of π/2 added to (or subtracted from) the angle a, is formed tothe sine of this angle. The same operations with the number of 3π/2 to givethe sine, taken with a negative sign. Accordingly, in the case that you are working with tothe sine ofω, then the sine will allow you to obtain the addition or subtraction of 3π/2, and its negative value of π/2.
Use formulas to find the sineor cosine ofa double angle to Express the sine through tothe sinus. The sine of a double angle is twice the product of the sineand cosine ofthis angle and tothe sine of twice the angle is the difference between the squares forthe sineand sine.
Pay attention to the possibility of recourse to formulas of sum and difference of sines and tothe sines of the two angles. If you perform operations with angles a and C, then the sine of their sum (difference) is the sum (difference) product of the sineof these angles s and tothe sine ofs, and tothe sine of the sum (difference) is the difference (amount) works forthe sines and sines angles, respectively.