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.