Scientific calculators have keys designed for trigonometric functions. They calculate the values of the sine, cosine, and tangent trigonometric ratios of any angle or determine the angle corresponding to the trigonometric value.
There are two models of scientific calculators, one with the MODE key and the other with the DRG key. We will demonstrate the operation of the calculator that has the MODE key.
There are equipments that work with three measurement units: degree, radian and grad. The choice for one of the measurements is made by pressing the MODE key and the chosen unit key: DEG (degree), RAD (radian) or GRA (grad). We will use the degree unit in our demonstration, then we will perform the following operation: press MODE and then DEG.
Given an angle of 35º, to obtain the value of its sine we type the value 35 and then the SIN key. In this case, the irrational number 0.5735764363510460961 will appear on the display... This means to say that sin35º = 0.573576..., an irrational number, as it is a non-periodic decimal.
If we choose the cosine or the tangent, we key in: 35 COS or 35 TAN, where we have cos 35º = 0.819152044288991789684... and tg 35º = 0.70020753820970977945852... To perform the inverse operation, that is, find the angle corresponding to the value of the trigonometric ratio, we type the value of sine, cosine or tangent and press the SHIFT and SIN keys–1. Look at the example:
What are the acute angles of a right triangle whose sides measure 9, 12 and 15 centimeters?
sinα = 9/15
Enter on your calculator 9: 15 = SHIFT SIN–1
the display will show 36.87º
cosβ = 9/15
Key 9: 15 = SHIFT COS–1
the display will show 53.13º
So the SIN and SIN keys–1, determine the following functions:
SIN gives the sine, cosine or tangent according to the angle value
SIN–1 gives the angle, according to the value of the trigonometric ratio.
by Mark Noah
Graduated in Mathematics
Brazil School Team
Trigonometry - Math - Brazil School
Source: Brazil School - https://brasilescola.uol.com.br/matematica/calculadora-cientifica-na-trigonometria.htm