So we need to get both of the argument of the sine and the denominator to be the same.
We can do this by multiplying the numerator and the denominator by 6 as follows.
All derivatives of circular trigonometric functions can be found using those of sin(x) and cos(x).
The quotient rule is then implemented to differentiate the resulting expression.
For example, the derivative of f(x) = sin(x) is represented as f ′(a) = cos(a).
Differentiation Of Trigonometric Functions Homework Answers
f ′(a) is the rate of change of sin(x) at a particular point a.
Let θ be the angle at O made by the two radii OA and OB.
Since we are considering the limit as θ tends to zero, we may assume that θ is a very small positive number: The following derivatives are found by setting a variable y equal to the inverse trigonometric function that we wish to take the derivative of.
Before we start differentiating trig functions let’s work a quick set of limit problems that this fact now allows us to do. In fact, it’s only here to contrast with the next example so you can see the difference in how these work.
In this case since there is only a 6 in the denominator we’ll just factor this out and then use the fact.