Prepared: Thu Apr 29 16:48:41 CDT 1999

MATH 1151

QUIZ IV

1) Determine the value of the six trigonometric functions for in terms of x.

Using Pythagorean Theorem, we solve for b in terms of x:

Now use the definitions of sin, cos and tan in terms of opp, adj and hyp:

2) a) Express the angle in degree measure: .

Conversion from radians to degrees can be achieved by multiplying the angle by (multiply by degrees, divide by radians):

b) Express the angle in radian measure: .

Conversion from degrees to radians can be achieved by multiplying the angle by (multiply by radians, divide by degrees):

3) Find the angle in between the hour hand and the minute hand of a clock at 10:30pm.

Consider the hour hand first. At 12pm the hour hand points 12, so let's choose 12 as the starting point. The hour hand completes one revolution in 12 hours, that means in 12 hours and in 1 hour. At 10:30, already 10.5 hours have passed and this corresponds to . But be careful here, is the angle between the hour hand and the starting point.

Now, consider the minute hand. It completes one revolution in 60 minutes, i.e. in 60 minutes which corresponds to in 1 minute. Already 30 minutes have passed, so the angle between the minute hand and the starting point is .

To find the angle between the hour hand and the minute hand, just subtract the smaller from the bigger one: .

4) Given and find , , and .

Remember the formula

and the reciprocal formulas. We do not even need to picture a right triangle.