Instruction

1

Use the knowledge of plane geometry to Express

**the sine**through to**the sinus**. According to the definition,**the sine**of the th angle in a right triangle is the ratio length opposite side to hypotenuse, and**sine**om – 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.2

Express

**the sine**through to**the 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.3

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 to

**the sine**of this angle. The same operations with the number of 3π/2 to give**the sine**, taken with a negative sign. Accordingly, in the case that you are working with to**the sine of**ω, then**the sine**will allow you to obtain the addition or subtraction of 3π/2, and its negative value of π/2.4

Use formulas to find

**the sine**or co**sine of**a double angle to Express**the sine**through to**the sinus**. The sine of a double angle is twice the product of the**sine**and co**sine of**this angle and to**the sine of**twice the angle is the difference between the squares for**the sine**and**sine**.5

Pay attention to the possibility of recourse to formulas of sum and difference of

**sine**s and to**the sine**s 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 sine**of these angles s and to**the sine of**s, and to**the sine**of the sum (difference) is the difference (amount) works for**the sine**s and**sine**s angles, respectively.