section 4.1
Trigonometric functions are used to find the side lengths and angles of triangles.
You can use SohCahToa to remember these.
Inverse trig functions are used to determine angles. For example, if you are given a triangle with two sides, one being the opp and the other the adj, then you know one angle is a right angle and are asked to find the other two angles, this is where inverses come in handy.
section 4.2
DSM and Decimal Degree Form: we learned how to convert degrees into minutes and seconds.
Example: 56.735...
first you take 0.735 and multiply it by 60. which gave you 44.1 so then you take that 0.1 and multiply it by 60 as well getting 6.
then you piece it all together for a final answer of 56 degrees 44 minutes and 6 seconds. to go backwards you keep your 56 then add 44 times 1/60 plus 6 times 1/3600.
Example: 56.735...
first you take 0.735 and multiply it by 60. which gave you 44.1 so then you take that 0.1 and multiply it by 60 as well getting 6.
then you piece it all together for a final answer of 56 degrees 44 minutes and 6 seconds. to go backwards you keep your 56 then add 44 times 1/60 plus 6 times 1/3600.
Next we went over radian measures
Next we learned the degrees and radians conversion rules.
If you want to go from degrees to radians you multiply by pi radians/180
and if you want to go from radians to degrees you multiply 180/pi radians
If you want to go from degrees to radians you multiply by pi radians/180
and if you want to go from radians to degrees you multiply 180/pi radians
Coterminal Angles are when there is an angle and you can add 360(n) to it and any answer you get can be a coterminal angle with the original. Example: 45 is coterminal with 405 because 45+360(1) is 405.
Arc Length is found by multiplying the measure of the angle by the radian.
Arc Length is found by multiplying the measure of the angle by the radian.
Next we learned how to find the area of a sector on a circle.
This can be used to find the area of any section of a triangle when given the angle measure.
section 4.3
trig functions at any angle.
These can be used to determine what the different ratios would be for different triangles.
On the unit circle the radius will always be one.
The y is sin and the x is cos.
Common rules for finding reference angles in a circle are:
On the unit circle the radius will always be one.
The y is sin and the x is cos.
Common rules for finding reference angles in a circle are:
The quadrants are:
X or theta in the equations are the different angle measures, so you just plug those in and then solve.
Trig functions on the unit circle:
The unit circle is used to find all the different values of each trig function for triangles and angles.
section 4.4
Properties of sine and cosine functions:
When graphing sine and cosine:
y=a(bx+c)
Amplitude: |a|
Period: 2π÷|b|
Frequency: |b|÷2π
Phase Shift: -c÷|b|
y=a(bx+c)
Amplitude: |a|
Period: 2π÷|b|
Frequency: |b|÷2π
Phase Shift: -c÷|b|
section 4.5
Properties of tangent functions:
Period: pi/|b|
Properties of cotangent functions:
Properties of cotangent functions:
Cosecant Graphs:
Secant Graphs: