Notes for Homework 9, due March 27

Working on Asin(bx + c) + D

Defining the function given two consecutive extremes

Notes for Homework 8, due March 20

Notes on Law of Sines and Law of Cosines

Notes for Homework 7, due March 13

The Law of Cosines to find a third side length

The Law of Cosines to find three angles given three sides

More on the Law of Cosines to find three angles given three sides

Notes for Homework 6, due March 6

Notes for double angle and addition and subtraction of angles

Typo on take home midterm

On the top problem on the back page, the angle has a negative value for cosine, but we are told it is in Quadrant IV. Cosine is positive in Quadrant IV. Instead change the question to say Quadrant III instead.

Notes for Homework 5, due Monday, Feb. 27

Degrees to DMS: Most scientific calculators has a function that will take a decimal number and convert it to degrees, minutes and seconds. Degrees and minutes will be whole numbers, but seconds might be a decimal. Not all the calculators round the seconds decimal to the same level, so I ask that it be rounded to the nearest tenth.

Example: if we take the inverse sine of 1/3, we get 19.47122063...°,which I ask to be rounded to four places after the decimal, so 19.4712°. If we take the unrounded answer and find the DMS conversion, we get 19° 28' 16.394" when using the TI-83 and 19° 28' 16.4" when using the TI-30XIIs. Because these calculators made by the same company don't round to the same level, I ask for the rounding to be to the nearest tenth of a second.

Note: Inverse sine and inverse tangent of negative numbers give negative angles in Quadrant IV. Add 360° to get a number between 0° and 360°.

Degrees to radians, both as a decimal number and a decimal time pi. At this point in the semester, your calculator should be DEGREE mode, so on any of the problems on the homework should start with taking the requested inverse trig function, converting the answer to a positive angle if necessary. Whether you have the angle in decimal degrees or DMS, you can now multiply the answer by pi/180 to get radians as a decimal number. In this case, you should get 0.339836909..., which I ask to be rounded to .3398. If you divide this by pi, you get .108173448..., which is the decimal number to be multiplied by pi. This means the four answers to the inverse sine of 1/3 are

Decimal degrees: 19.4712°
DMS: 19° 28' 16.4"
Radians: .3398
Radians as a multiple of pi: .1082pi

   

Notes for Homework 4, due Wed. Feb. 22

The trig values for the "famous" angles of the first quadrant and (1, 0) and (0, 1), part 1


The trig values for the "famous" angles of the first quadrant and (1, 0) and (0, 1), part2

Changing angles to radians

 

Notes for Homework 3, due Monday Feb. 13

Practice finding all trig values given one value, assuming all the values are non negative.

Practice for making denominators radical free.
 
Working with fractions with denominators of the form a + sqrt(b).

1)  3/(1 + sqrt(7))

2) 4/(sqrt(6) + 2)

3) 12/(sqrt(10) - 2)

Answers to the last three in the comments.

Notes for Homework 2, due Monday, Feb. 6

Classification of a triangle defined three vertices

The trig values for the "famous" angles: 0°, 30°, 45,°, 60° and 90° 

Rationalizing the denominators of fractions with square roots

Practice for Homework 1, due January 31

Heron's Formula practice #1

Heron's Formula practice #2 

Classification of triangles by angle 

Classification of triangles by side length