## 11-12 Two trains; one going to east, and the other is heading north

Problem 11
A train starting at noon, travels north at 40 miles per hour. Another train starting from the same point at 2 PM travels east at 50 miles per hour. Find, to the nearest mile per hour, how fast the two trains are separating at 3 PM.

Problem 12
In Problem 11, how fast the trains are separating after along time?

## 10 - A boy on a bike

Problem 10
A boy on a bike rides north 5 mi, then turns east (Fig. 47). If he rides 10 mi/hr, at what rate does his distance to the starting point S changing 2 hour after he left that point?

## 06-07 Ladder slides down the wall

Problem 06
A ladder 20 ft long leans against a vertical wall. If the top slides downward at the rate of 2 ft/sec, find how fast the lower end is moving when it is 16 ft from the wall.

Problem 7
In Problem 6, find the rate of change of the slope of the ladder.

## Trigonometry

### Video

The Six Trigonometric Functions

1. $\sin \theta = \dfrac{a}{c}$
2. $\cos \theta = \dfrac{b}{c}$
3. $\tan \theta = \dfrac{a}{b}$
4. $\csc \theta = \dfrac{c}{a}$
5. $\sec \theta = \dfrac{c}{b}$
6. $\cot \theta = \dfrac{b}{a}$