WEBVTT
00:00:02.530 --> 00:00:12.460
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.
00:00:12.790 --> 00:00:16.170
In this question, we’re asked to evaluate a trigonometric expression.
00:00:16.240 --> 00:00:19.220
And we need to give our answer to two decimal places.
00:00:19.500 --> 00:00:21.330
We’ll do this by using a calculator.
00:00:21.400 --> 00:00:23.410
Let’s start with our calculator screen.
00:00:23.710 --> 00:00:30.880
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.
00:00:31.130 --> 00:00:36.810
This is usually represented in the top-right corner with the letter D or DEG for degrees.
00:00:37.070 --> 00:00:43.030
If our calculator is not set to degrees mode, we need to change it into degrees mode by using the mode or setup menu.
00:00:43.460 --> 00:00:48.910
What this mode does is it tells us the type of angle we’re inputting into our functions.
00:00:49.180 --> 00:00:57.390
So, for example, if we type sin 33 into our calculator in degrees mode, then it knows that 33 is measured in degrees.
00:00:57.680 --> 00:01:03.840
This will then allow us to evaluate our trigonometric expression since all three of the angles are given in degrees.
00:01:04.140 --> 00:01:09.850
We might be tempted to find each of the three terms in this expression separately by using our calculator.
00:01:09.940 --> 00:01:13.650
However, remember, we need to be accurate to two decimal places.
00:01:13.960 --> 00:01:19.570
And doing it this way may lead to rounding errors if we don’t use the memory function in our calculator.
00:01:19.640 --> 00:01:23.040
So instead, we’ll find this entire expression at once.
00:01:23.350 --> 00:01:29.600
This means we need to type this entire expression into our calculator, keeping in mind the order of operations.
00:01:30.070 --> 00:01:31.990
There are a few different ways of doing this.
00:01:32.020 --> 00:01:34.740
We know that we’re taking the quotient of two values.
00:01:35.140 --> 00:01:40.610
This is a shorthand notation to mean that we evaluate the numerator and the denominator separately.
00:01:40.640 --> 00:01:45.190
So there should be an extra pair of parentheses above both the numerator and denominator.
00:01:45.190 --> 00:01:51.620
So the numerator of this expression is the sin of 31 degrees plus the cos of 25 degrees.
00:01:51.620 --> 00:01:54.360
And we’ve written this all inside a pair of parentheses.
00:01:54.640 --> 00:01:58.650
Then, we need to divide all of this by the sin of 33 degrees.
00:01:59.010 --> 00:02:05.170
This is just one possible expression we could type into our calculator to evaluate the trigonometric expression we’re given.
00:02:05.630 --> 00:02:08.050
So we start with one open parenthesis.
00:02:08.400 --> 00:02:11.950
We then click the sine button on our calculator to input the sine function.
00:02:12.310 --> 00:02:16.080
We then type 31 since this is the argument of this sine function.
00:02:16.270 --> 00:02:20.930
And it’s then very important to close the set of parentheses since this is the end of our argument.
00:02:21.260 --> 00:02:26.320
Next, we need to add the cosine function, which we find by clicking the cosine button on our calculator.
00:02:26.700 --> 00:02:29.120
The argument of this cosine function is 25.
00:02:29.120 --> 00:02:34.110
So we type this in, and then we close our parentheses since we’ve ended the argument of the cosine function.
00:02:34.350 --> 00:02:39.220
We then close our first set of parentheses since this is the end of the numerator of our expression.
00:02:39.560 --> 00:02:42.660
Finally, we click divide and enter sin of 33.
00:02:43.050 --> 00:02:45.080
Doing this, we get something like the following.
00:02:45.410 --> 00:02:48.450
We can then evaluate this expression by clicking the equals button.
00:02:48.880 --> 00:02:53.670
Doing this, we get 2.60970252.
00:02:54.000 --> 00:02:56.640
We need to give this value to two decimal places.
00:02:56.670 --> 00:02:59.870
So we need to look at the third decimal digit, which is nine.
00:03:00.200 --> 00:03:07.650
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.
00:03:07.800 --> 00:03:17.340
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.