1. Solve the right triangle.
Warm Up 10.2
If , find the value of the 5 other trig functions. Leave your answers in simplified radical form.
Solve the right triangle.
You measure the angle of elevation of a kite to be 79o. If the kite string is 500 feet long, how high is the kite?

2. Define general angles and use radian measure (13.2)
Unit 10: Trigonometric Ratios and Functions
Target 10.2
Define general angles and use radian measure (13.2)

3. An angle is said to be in standard position if its initial side lies on the positive ______________, and its vertex is at the ___________.
A positive angle tells you to rotate the terminal side of the angle _____________________. A negative angle tells you to rotate ____________________.
Sketch the indicated angle in standard position. Then state which quadrant (or axis) it lies in (or on).
a) 240o
d) 1080o
b) 500o
e) -190o
c) -50o

4. Sketch the indicated angle in standard position.
a) 150o
b) -210o
These two angles are said to be coterminal (since they share a terminal side). To find coterminal angles, simply add or subtract a multiple of __________.

5. Find one positive and one negative coterminal angle for each angle.
b) 395o
a) -45o

6. Radians are another way (as opposed to degrees) to measure an angle
Radians are another way (as opposed to degrees) to measure an angle. Radians are used frequently in trig.
One radian is the measure of an angle whose terminal side intercepts an arc of length r.
If you go all the way around the circle, how many radians would you have? In other words, what’s the circumference?
Thus, 360o is equal to ______ radians, and 180o is equal to _____ radians.

7. We will use the fact that 180o = π radians to convert angles back and forth. At first, it may be easier to always convert radians to degrees (since degrees are much more familiar), but you should start to get used to (i.e. memorize) the “important” radian measures.
Convert to radians.
300o
540o
Convert to degrees.

8. Find one positive and one negative angle that is coterminal with the given angle. (Instead of adding or subtracting multiples of 360, add or subtract multiples of 2π when working with radians).

9. Sketch the angle with the given radian measure.
90o a) b)
180o 0o
360o c)
These 4 angles are called quadrantal angles, and along with 30o, 45o, and 60o, they are very important to our study of trigonometry.
270o

10. This chart shows all the “important” angles in both degrees and radians. (There is also a chart like this in your book on Page 861). You don’t need to memorize it (this year), but it will be very useful to have as a reference.

11. Sin Cos Tan Csc Sec Cot 30o 45o 60o
Remember this chart from yesterday? Let’s add the radian measures to the chart as well.
Sin
Cos
Tan
Csc
Sec
Cot
30o
45o
60o
We can use this chart to find exact values of the 6 trig functions (as we did yesterday) for these special angles. If the angle is not one of the three listed above, we will use our calculator to get an approximate answer (make sure you are in radian mode!)

12. Evaluate. When possible, give exact answers.

13. Remember arc lengths and areas of sectors from geometry
Remember arc lengths and areas of sectors from geometry? We can use radians to quickly calculate these values.
*Note: Your angle must be measured in radians!

14. A softball field forms a sector with the dimensions shown
A softball field forms a sector with the dimensions shown. Find the length of the outfield fence and the area of the field.