Question Video: Calculating the Sum of the Sine and Cosine Function of Given Angles Mathematics

Calculate sin (18° 35′) + cos (18° 35′), giving your answer to two decimal places.

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Video Transcript

Calculate sin of 18 degrees 35 minutes plus cos of 18 degrees 35 minutes, giving your answer to two decimal places.

In this question, we are asked to calculate a trigonometric expression where the argument is given in degrees and minutes. Before typing anything into our calculator, we must ensure that we are in the correct mode. In this question, we need to be in degree mode, denoted by the letter D in the top right-hand corner of our calculator screen.

As already mentioned, the arguments here are given in degrees and minutes. We have two options here. Either we can convert these into just degrees, or we can use the degrees, minutes, and seconds button on the calculator. If we decide to use this button, we begin by simply pressing the sin key. We then type the first part of our argument, 18. Next, we press the degrees, minutes, and seconds button. We then type the remainder of the argument, 35, and press the degrees, minutes, and seconds button once again. After closing the parentheses, we can press the equals button to evaluate this. The sin of 18 degrees 35 minutes is equal to 0.31868 and so on. We can then repeat this for the cosine of the same angle. The cos of 18 degrees 35 minutes is equal to 0.94786 and so on.

We need to calculate the sum of these values. This is equal to 1.26654 and so on. We are asked to give our answer to two decimal places. As the third digit after the decimal point is a six, we round up. The sin of 18 degrees 35 minutes plus the cos of 18 degrees 35 minutes is equal to 1.27 to two decimal places.

As mentioned earlier, an alternative method would be to convert 18 degrees 35 minutes into just degrees. If an angle is equal to 𝑑 degrees and 𝑚 minutes, this is equal to 𝑑 plus 𝑚 over 60 degrees, as there are 60 minutes in a degree. In this question, 18 degrees 35 minutes is equal to 18 plus 35 over 60 degrees. This is equal to 18.5833 and so on degrees.

We could therefore calculate the sine of this angle, the cosine of this angle, and then the sum of these values. This would once again give us an answer of 1.27 to two decimal places.

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