Video Transcript
Calculate the sin of 18 degrees, 35 minutes multiplied by the cos of 18 degrees, 35 minutes, giving your answer to two decimal places.
In this question, we’re asked to calculate a trigonometric expression where the angle or argument is given in degrees and minutes. We begin by ensuring that our calculator is in degree mode. This is denoted by the letter D in the top right-hand corner of our screen. One way of answering this question is to type the calculation directly into our calculator using the degrees, minutes, and seconds button. We begin by pressing the sin button. We then type the first part of our argument, 18, followed by the degrees, minutes, and seconds button. After typing 35, we press this button again as shown. Next, we close the parentheses. We then repeat this process to type the cos of 18 degrees, 35 minutes. We can now press the equals button to evaluate our expression. The sin of 18 degrees, 35 minutes multiplied by the cos of 18 degrees, 35 minutes is equal to 0.30206 and so on.
We’re asked to round our answer to two decimal places. As the third digit after the decimal point is a two, we round down. sin of 18 degrees, 35 minutes multiplied by cos of 18 degrees, 35 minutes is equal to 0.30 to two decimal places.
An alternative method here would be to convert our angle or argument into just degrees. We recall that 𝑑 degrees and 𝑚 minutes is equal to 𝑑 plus 𝑚 over 60 degrees, since there are 60 minutes in one degree. 18 degrees and 35 minutes is therefore equal to 18 plus 35 over 60 degrees, which is equal to 18.5833 and so on degrees. We could therefore type the sine of this angle multiplied by the cosine of this angle into our calculator, which once again gives us an answer of 0.30 to two decimal places.
