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

vectors and angles

Here are some two dimensional vectors. Find the difference between the vectors, both U-V and V-U, the dot products U·U, V·V, U·V, length of the vectors and the cosine of the angle between them, which is given by the formula in the picture above.

Example

U = <4 3> and V = <0 5>

U·U =  25

V·V =  25

U·V = 15

||U|| = sqrt(25) = 5

||V|| = sqrt(25) = 5

costheta = 15/25 = 3/5

theta ~= 53.1301°

Practice.

U = <4 3> and V = <3 -4>

U·U = ______

V·V =  ______

U·V =______

||U|| = ______

||V|| = ________

costheta = ______

theta = _______

U-V = _______

||U-V|| = _________

cosine of angle between U and U-V = ________


angle to nearest thousandth of a degree = _______


V-U = _______

||V-U|| = _________

cosine of angle between V and V-U = ________


angle to nearest thousandth of a degree = _______



Answers in the comments.

Practice problems similar to take home

a) Rewrite cos^4(alpha) - sin^4(alpha) in a simpler form with lower powers of the trig functions

b) let cosgamma = 5/7 find
singamma
tangamma
cos(½gamma)
sin(½gamma)
tan(½gamma)
cos(2gamma)
sin(2gamma)
tan(2gamma)

c) The sides of a triangle are A = 5, B = 5 and C = 8.

Find the area.
Find the approximate value of alpha in degrees, rounded to four places after the decimal.
Find the approximate value of beta in degrees, rounded to four places after the decimal.
Find the approximate value of gamma in degrees, rounded to four places after the decimal.
Find the height if A is the base.
Find the height if B is the base.
Find the height if C is the base.

d) A = 6, B = 7, beta = 90° Find sinalpha and alpha written in degrees rounded four places after the decimal.

Answers in the comments.

Practice problems for Homework 10

Find the high point and low point surrounding the median point closest to (0, 0) for the following trig functions.

f(x) = 6sinx - 8cosx

g(x) = 2sinx - 4cosx

Here are three points on the unit circle in the complex plane.  Multiplying two points of the form costheta + isintheta and cosiota+isiniota gives us the values for the angle theta + iota.

a = 1/5 + i2sqrt(6)/5
b = 2/5 + isqrt(21)/5

ab =

a² =
a³ =

Answers in the comments.