Week 10

This week we started Chapter 4, Trigonometric Functions.

We started on Day on, Angles and their Measurements. This lesson was review from Algebra 2 except for a few elements that was added in.

Trigonometry is practically all about triangesl inside circles and that is what we will be looking at for the next few weeks and months.

We began at standard position, which is the initial side on the positive x-axis.

We then looked at coterminal angles, which are angles that have the same terminal line.

ex: 960°

this could be 240° or even -120° 

Then Minutes and Seconds 

1°= 60' (minutes)

1°=3600" (seconds)

We then looked at Radian Measures.

θ= S/r

S= Sector 

θ=angle

r=radius

To convert degrees to radians:

You times the degree by π/180

radians to degrees: 

180/π

We then looked at complementary and supplementary

For Complementary:

you add 90°

or add π/2

ex:  θ= 74.23°

74.23 + x = 90

You then solve for x and you find the complementary angle.

For Supplementary:

you add 180°

or add π

ex: π/3 radians

π/3 + x = π

You then solve for x 

Lastly, we looked at arc lengths: Arc lengths.

Degrees has to converted to radians beforehand to be solved

The equation is: S=rθ

Almost all of this is review from Algebra 2 except for a few, but they are mostly self-explanatory.

On day 2, we looked at Sine and Cosine Functions. 

We had a look again at the identities of the Sine and Cosine Functions from last year. 

Just one thing before we start: COS= x    Sin= y.

Below is a graph of what of a triangle and how sine and cosine works.

On the side are a few of the Identities:

sin θ = opp/ hyp         csc θ = hyp/ opp

cos θ = adj/ hyp         sec θ = hyp/ adj

tan θ = opp/ adj         cot θ = adj/ opp

other identites: 

tan θ= sin θ / cos θ

cot θ= cos θ / sin θ

csc θ= 1 / sin θ

sec θ= 1 / cos θ

An important identity is the pythagorean thereom: a^2+b^2= c^2

It practically is 

x^2+y^2=r^2

x^2+y^2=1

this can translate to 

cos^2 θ + sin^2 θ = 1

This is called the Pythagorean Identity.

After this we looked at the acrynom: All Students Take Calc.

From this acrynom, it states where the functions are postive. in the A box, all the functions are positive. In S, Sine and cosecant are positive. In T, tangent and cotangent are positive. In C, Cosine and Secant are positive. 

Next we looked at reference angles: To find the reference angle, you just drop a line from the angle and you find the measurement from the angle. 

Some More Identities:

cos(-t) = cos t

sin(-t) = -sin t

cos(π/2 -t)=sin t           sin(π/2 -t)= cos t

cos(t + π) = -cos t        sin(t+π) = -sin t

cos(π - t) = -cos t        sin(π - t) = sin t

Now to solve problems: 

 ex 1: 

If you were looking for sin θ: cos θ= -2/5

Point, P in II Quadrant

1. you first sketch it on a graph

2. sinθ =O/H

a^2+ (-2)^2 = 5^2

a^2 + 4 = 25

a^2 =21

a^2 = √21

sinθ = √21 / 5

ex 2: Angle: -7π/4   Find the Reference Angle

1. Drop a line to the x-axis from the angle

It would then be 9π/20

This is what we looked at this week. We reviewed after this and then took a quiz on the last day.

SEE YOU NEXT WEEK!