HW

Make sure your calculator is in degrees mode.  To check, hit the MODE button and look for the row (3rd down?) which reads "radian degree".  If "degrees" is not highlighted, scroll down to it and hit ENTER.  Then close MODE by hitting 2ND MODE.

1.  What is the index of refraction for a substance that slows light down to half its speed in a vacuum?

(2)

2.  What is the index of refraction for a substance that takes an initial light ray in air at 50 degrees (WRT to a normal line) and bends it to 34 degrees?

(1.37)

3.  A light ray hits a block of plexiglass (n = 1.65) at 45 degrees.  What is the angle of refraction inside the block?

(25.5 degrees)

Trig Practice, if you need it.

Consider a 5-12-13 right triangle.

1.  Draw this.  Let the 5 side be horizontal (adjacent side).  13 is obviously the hypotenuse and 12 is the opposite side.

2.  So that we are on the same page, consider your reference angle as the angle between 5 and 13.

3.  Find the values for sin, cos and tan of the reference angle.

(12/13, 5/13, 12/5)

4.  Use the 2ND SIN function to find the angle itself.  (You could also use 2ND COS or 2ND TAN.)

2ND SIN (12/13) = 67.38 degrees

5.  Repeat this for an 8-15-17 triangle, if you have time.

FYI:  https://en.wikipedia.org/wiki/Pythagorean_triple



Part 2.  Calculator practice.  Find these:

1.  sin 0

(0)

2.  sin 30

(0.5)

3.  sin 45

(0.707)

4.  sin 60

(0.866)

5.  sin 90

(1)

6.  cos 0

(1)

7.  cos 45

(0.707)

8.  cos 60

(0.5)

9.  cos 90

(0)

Inverse practice.  Find the angle, knowing that:

1.  sin (theta) = 0.6

(36.9 degrees)

2.  sin (theta) = 0.25

(14.5 degrees)

3.  cos (theta) = 0.75

(41.4 degrees)

(If you've forgotten how to do these, recall the part about the 2ND SIN (or 2ND COS) functions.)

Probably the most important thing to remember here is what sine, cosine, and tangent actually represent -  they are RATIOS of sides associated with a particular angle.  For example, if a right triangle has a 30-degree angle in it, the sine of that angle (0.5) tells us that the ratio of the length of the side opposite that angle to the length of the hypotenuse is 0.5.

On the other hand, if we only knew the sine value (or cosine or tangent value), we could use that information to find the angle itself.  In the old days, you'd look up a value in a big chart.  Now, your calculator goes through an algorithm to solve for the angle.