# 6.3: Derivatives of Other Trigonometric Functions

- Page ID
- 106370

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This optional summary video from the textbook author might be helpful to use as a preview. Other, more detailed, supplemental videos for this section are posted at the end of the text.

## Supplemental video

## Homework Exercises 6.3

### WeBWorK Problems:

### Written Problems:

**1.** Find the equation of the tangent line to the curve \(y=3tan(x)\) at the point \((\frac{pi}{4}, 3)\). You may leave your answer in point slope form without simplifying to \(y=mx+b\).

**2. **An object moving vertically has its height at time *t* (measured in feet, with time in seconds) given by the function \(h(t)=3+\frac{2cos(t)}{1.2^t}\).

**a. **What is a function that describes the object's instantaneous velocity at any time?

**b. **Find the approximate (to two decimal places) instantaneous velocity of the object at *t* = 2 and at *t* = 2.1

**c. **Describe in everyday language the behaviour of the object at the instant *t* = 2. Make sure to include the speed, direction, and whether it is slowing down or speeding up. It might be helpful to look at the graph of *h(t)* at *t* = 2. Also note what the sign of the second derivative of *h*(*t*) should be.