Trigonometry and Wave Function Flashcards
π radians =
180 degrees
30 degrees in radians
π/6 radians
45 degrees in radians
π/4 radians
60 degrees in radians
π/3 radians
90 degrees in radians
π/2 radians
135 degrees in radians
3π/4 radians
360 degrees in radians
2π radians
how to convert from degrees to radians
multiply by π and divide by 180
how to convert from radians to degrees
multiply by 180 and divide by π
describe exact values triangle for 45 degrees
right angled triangle
45 degrees at each of other vertices
root 2 on hypotenuse
1 on other sides
describe exact values triangle for 30/60 degrees
right angled triangle
1 along base
2 on hypotenuse
root 3 on other side
60 in angle between 1 and 2
30 in angle between 2 and root 3
how to work out exact values for 0,90,180,360 etc.
trig graphs
when would there be no solutions for sin/cos
has to be greater than or equal to -1 and less than or equal to 1
what does sin2x mean?
there are 2 cycles of sin graph in 360 degrees
what part of the question should you pay close attention to when deciding how many answers are required?
the domain
if there is a squared term what should you remember
that it could be positive or negative when you square root so will need to work out solutions in all quadrants
what should be noted if an angle is acute?
a cast diagram is not necessary
what is the result when we add or subtract angles?
a compound angle
sin (A+B) =
sinAcosB + cosAsinB
sin (A-B) =
sinAcosB - cosAsinB
cos (A+B) =
cosAcosB - sinAsinB
cos (A-B) =
cosAcosB + sinAsinB
how to layout question asking you to prove one of the compound angle formulas using given numbers
work out LHS and RHS separately then state “since LHS=RHS, the claim it true for…”
how to find the exact value of sin75
sin(45+30)