Question Video: Using a Calculator to Evaluate an Expression Involving Values of Trigonometric Functions Mathematics

Calculate (sin (31°) + cos (25°))/sin (33°), giving your answer to two decimal places.


Video Transcript

Calculate the sin of 31 degrees plus the cos of 25 degrees all divided by the sin of 33 degrees, giving your answer to two decimal places.

In this question, we’re asked to evaluate a trigonometric expression. And we need to give our answer to two decimal places. We’ll do this by using a calculator. Let’s start with our calculator screen. Whenever we’re asked to evaluate a trigonometric expression by using a calculator, we should always check that our calculator is set to degrees mode. This is usually represented in the top-right corner with the letter D or DEG for degrees. If our calculator is not set to degrees mode, we need to change it into degrees mode by using the mode or setup menu. What this mode does is it tells us the type of angle we’re inputting into our functions. So, for example, if we type sin 33 into our calculator in degrees mode, then it knows that 33 is measured in degrees. This will then allow us to evaluate our trigonometric expression since all three of the angles are given in degrees.

We might be tempted to find each of the three terms in this expression separately by using our calculator. However, remember, we need to be accurate to two decimal places. And doing it this way may lead to rounding errors if we don’t use the memory function in our calculator. So instead, we’ll find this entire expression at once. This means we need to type this entire expression into our calculator, keeping in mind the order of operations.

There are a few different ways of doing this. We know that we’re taking the quotient of two values. This is a shorthand notation to mean that we evaluate the numerator and the denominator separately. So there should be an extra pair of parentheses above both the numerator and denominator. So the numerator of this expression is the sin of 31 degrees plus the cos of 25 degrees. And we’ve written this all inside a pair of parentheses. Then, we need to divide all of this by the sin of 33 degrees. This is just one possible expression we could type into our calculator to evaluate the trigonometric expression we’re given.

So we start with one open parenthesis. We then click the sine button on our calculator to input the sine function. We then type 31 since this is the argument of this sine function. And it’s then very important to close the set of parentheses since this is the end of our argument.

Next, we need to add the cosine function, which we find by clicking the cosine button on our calculator. The argument of this cosine function is 25. So we type this in, and then we close our parentheses since we’ve ended the argument of the cosine function. We then close our first set of parentheses since this is the end of the numerator of our expression.

Finally, we click divide and enter sin of 33. Doing this, we get something like the following. We can then evaluate this expression by clicking the equals button. Doing this, we get 2.60970252. We need to give this value to two decimal places. So we need to look at the third decimal digit, which is nine. Since this value is greater than or equal to five, we need to round this value up, which gives us 2.61, which is our final answer. Therefore, the sin of 31 degrees plus the cos of 25 degrees all divided by the sin of 33 degrees to two decimal places is 2.61.

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