Math for the 100th time
Opposite of cotangent
(Cot) or cotangent
Opposite of sin
(Csc) or cosecant
Opposite of cosine
(Sec) or secant
Finding quadrants with radians
1/2 pie on top 1 pie on left 1 1/2 pie on bottom 2 pie on right
Pie over 6=
30 degrees
Pie over 4=
45 degrees
Pie over 3=
60 degrees
Co-terminal angle in radians (positive)
Add 2 pie Get common Denominator Add numerators across
Co-terminal angle to a degree (positive)
Add 360
Reference angles
Always positive Acute 0-90 degrees X Axis Example: (640 degrees) Plot where degree would be Look where the nearest x axis is (720) Subtract nearest x axis with original degree (640) Reference angle= 80 degrees For radians do the same thing Find where point lies based on the radians (17 pie/3) Look for nearest x axis (18 pie/3) Look to see how much is left over from the original radian to the x axis (pie/3)
Cos
Cah (adjacent over hypotenuse)
Drawing angles Quadrant in which terminal side of the angle lies
Draw dot in center Straight line through zero to the right Start circle in middle of line Draw line where angle would be Make into arrow
Trig values if given 1 trig value
It will always say if y is greater than or less than 0 If sin is less than 0 than y is negative If sin is greater than o y is positive Find where triangle belongs Draw a right triangle based on the points Label side opposite, adjacent, hypotenuse Label r as the side that is missing Use progatherim theorem to solve or r (numbers squared equals r squared) Take square root Simplify square root if possible Using SOH CAH TOA, write sin, cos, tan, sec, csc, and cot No radicals on the bottom Multiple by radical on top and bottom
Angle measures
Label sides opposite, adjacent, and hypotenuse Find what trig function involves the two sides Write trig function with missing x angle with it (cos x degrees) Write sides over eachother in the proper set up with its trig function Divide the fraction Take inverse of what the fraction equals Round to nearest whole number Write in degrees
To find length of side
Lable opposite, adjacent, and hypotenuse Find what trig function involves the two sides (including x) Write trig function with degree angle equal to x over a number or number over x Find the trig vale of the degree, write it round to 4 decimal places Cross multiple Solve for x Round to nearest 10th
Co-terminal angle in radians (negative)
Make radian number found in positive negative Add numerators across
Radians to degrees
Pie on top means use 180/pie Cancel pie Simplify numerators and denominators
Convert degrees to radians
Put degree over 1 Use pie over 180 Simplify numerators and denominators Multiply across
What does the hypotenuse always equal in the progatherium theorem?
R2
Negative radians
Same as above just negative
Sin
Soh (opposite over hypotenuse)
Cos of x column going down
Square root of 3/2 Square root of 2/2 1/2
Tan of theta column going down
Square root of 3/3 1 Square root of 3
Negative
Start at zero line go below and go to the left (clockwise) -270 on top -180 on left -90 on bottom -360 on the right
Positive
Start at zero line go to the left (counter clock wise) 90 at top then 180 to left 270 at the bottom 360 on right
Co-terminal angle to a degree (negative)
Subtract 360 if still positive, subtract 360 again
Chart (categories)
Theta, Cos of theta, sin of theta, tangent of theta
Tangent
Toa (opposite over adjacent)
Quadrants
Upper right quadrant is 1 Upper left 2 Bottom left is 3 Bottom right is 4
Trig value if given a point
Write coordinates as x and y Draw a right triangle based on the points Label side opposite, adjacent, hypotenuse Label r as the side that is missing Use progatherim theorem to solve or r (numbers squared equals r squared) Take square root Simplify square root if possible Using SOH CAH TOA, write sin, cos, tan, sec, csc, and cot No radicals on the bottom Multiple by radical on top and bottom
Cos of theta
X value
Sin of theta
Y value
Tangent of theta
Y/X value
Sin of y column going down
x column backwards 1/2 Square root of 2/2 Square root of 3/2
