what does "exact value" mean in trigonometry?

Question

for example: find the exact value of cos(x)sin(x) / tan(x). this is just an example. what does it mean to find the exact value of something in trig.?

Answer 1

It means if the answer is sqrt(3), then write the answer as
sqrt(3) and not 1.73.

cos(30) = sqrt(3)/2
Your calculator may give you
cos(30) = 0.866025403784
The exact value is sqrt(3)/2
The approximate value is 0.866025403784

Answer 2

When an instructor asks for an 'exact value', they are trying to keep you from using a calculator value.

For example: Sin(45 degrees) is sqrt(2)/2. If you just plugged it into your calculator, you would get something close to .707. But, the number is irrational and you could never write down the exact value.

There are some pretty standard angles that students are expected to know the trig functions of. These include:

0, 30, 45, 60, 90, 120, 135, 150, 180.

Sin(0) = 0 Cos(0) = 1 Tan(0) = 0
Sin(30) = 1/2 Cos(30) = sqrt(3)/2 and Tan(30) = Sin(30)/Cos(30)
Sin(45) = sqrt(2)/2 = Cos(45) and Tan(45) =1
Sin(60) = sqrt(3)/2 Cos(60) = 1/2 and Tan(60) = Sin(60)/Cos(60)
Sin(90) = 1 Cos(90) = 0 Tan(0) is undefined.

So, when an instructor asks for the exact value, they are asking for it in terms of these guys instead of just reading the answer off of your calculator.

Example: Find the exact value of Cos(30)*Sin(30)/Tan(30)

=1/2 * sqrt(3)/2 * 1/Tan(30). But, 1/Tan(30) is the same as
Cos(30)/Sin(30).

We get 1/2 *sqrt(3)/2 * 1/2/(sqrt(3)/2)
= 1/2 *sqrt(3)/2 * 1/sqrt(3) = 1/4.

Answer 3

The number before you do any thing to it so the exact value of (-2) is 2

Answer 4

It usually means as a fraction or non-repeating, finite, decimal. An example of a non-repeating infinite decimal is pi (3.14159...), where as a finite value is something like .5 (1/2). If the problem doesn't give you numbers, try cancelling. For instance, cos(x)sin(x)/tan(x) cancels to (cos(x))^2

Answer 5

It would mean the non-calculator answer. So your answer should be one of (or combination of) the common trig values that you learn. This means that you may have square root of 2 or 3 in your answer or pi.

Answer 6

"Exact value" means to leave your answer in radical form (if it's not rational) or in terms of π if you're dealing with radians.

cos(60°) = 0.5 is a valid answer, because it is 1/2.
sin(60°) = 0.866 is not exact... it's a rounded value.
The exact value of sin(60°) would be (√3)/2.

Answer 7

cos(x)sin(x)/tan(x) = cos^2(x)

The exact value is obtained when x is substituted.

Answer 8

the answer should be given either in the form of cos inverse (x) for example or in surds form when roots are involved.