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When it comes to differentiating, polar coordinates are more convenient because a derivative gives the slope of the tangent to a curve at some specific point. Since a curve is round, it makes more sense to use a circular approximation than a rectangular approximation, for sake of accuracy and precision. This doesn't make too much of a difference in terms of derivatives, but once you start hitting integrals, differentials, partials derivatives, and gradients of multivariable functions, you'll definitely want to be using radians instead of degrees.

Also, radians are generally preferred because they are all related by a factor of pi, a natural number, instead of 180 degrees, an arbitrary number, which makes them easier to calculate without a calculator (than degrees).

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Q: Why use radians when differentiating trig functions?
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What does evaluate the expression in both radians and degrees mean?

Radians and degrees are two different systems for measuring the size of an angle. In radians, a full circle is 2pi radians. In degrees, a full circle is 360 degrees. If you want to evaluate an expression in both, then first simplify and evaluate the expression plugging in radian values into your trig functions. The second time, use degree values. On your calculator, you can switch modes between radians and degrees. It should give you the same answer unless you are supposed to leave it written as unevaluated trig functions or something like that. To convert from radians to degrees... radians=degrees * (pi/180)

When do we use trig functions?

Trigonometry functions are used to work out the various properties of triangles.

How do you use cosine?

cosine = adjacent/hypotenuse. It can be used as other trig functions can.

What radian measure is equivalent to negative 15 degrees?

To convert from degrees to radians, you can multiply by (pi / 180). Or use the Excel function to convert from degrees to radians. I am not sure about the name; you can find it under math functions.

How do you calculate trignometric angle using java?

I assume you want the trigonometric functions. You can use the functions in the Math class. For example, if the variable "x" contains an angle, you can use Math.sin(x), Math.cos(x), etc., and if you want the angle from a sine stored in "y", Math.asin(y), etc. Note that, as in most programming languages, angles must be specified in radians. The Math class also contains functions to convert from degrees to radians, and from radians to degrees.

When use radians?

Whenever you are not able to use degrees you use radians instead

How do trigonometry used in our daily life?

That depends on your profession. If you are a math teacher, then you might use a lot of Trig. If you are an engineer, working with forces on any object from different directions, then you would use trig. Electrical engineers use trig. Surveyors use trig.

Uses of trigonometric functions in real life situations?

Can you use trigonomic functions in real life situations? It's not like you carry a calculator with you everywhere... Very unlikely unless you have a job that requires trig skills.

How do astronomers use trig in there work?

spherical trig look it up its way confusing

What is the use of differentiating a polynomial by 3 times?

If the original polynomial represents a position as a function of time, differentiating once will give you the speed, differentiating once more, acceleration. Differentiating a third time will give you the rate of change of acceleration; this is sometimes used, though not very frequently. One application where different functions are differentiated not just three times, but an arbitrary number of times, is to evaluate the function value, using Taylor's method.

What is a trig function?

sin theta and csc theta are reciprocal functions because sin = y/r and csc = r/y you use the same 2 sides of a triangle, but you use the reciprocal.

How do you input trigonometric functions in Microsoft Excel?

You can use the Insert Function button and choose the Math and Trigonometry category. From there you can pick the function you need and enter it in. All the main ones are there. You can enter in the radians using the PI function. So to get the SINE for 45° you would enter it as follows: =SIN(45*PI()/180) You can also use the RADIANS function: =SIN(RADIANS(45))