Exact Trig and graphs Flashcards
what is Sin 0?
0
what is Sin 30?
1/2
what is Sin 45?
1/ root2
what is Sin 60?
root3 / 2
what is Sin 90?
1
what is Cos 0?
1
what is Cos 30?
root3 / 2
what is Cos 45?
1 / root2
what is Cos 60?
1 / 2
what is Cos 90?
0
what is Tan 0?
0
what is Tan 30?
1 / root3
what is Tan 45?
1
what is Tan 60?
root3
what is Tan 90?
undefined
what are the features of a sine graph?
- repeats every 360 degrees
- period (wavelength) of 360 degrees
- maximum values at 90, 1
- minimum values at 270, -1
what are the features of a cosine graph?
- repeats every 360 degrees
- period (wavelength) of 360 degrees
- maximum values at 0, 1
- minimum values at 180, -1
what are the features of a tan graph?
- period is 180 degrees
- asymptotes at 90 and 270 degrees
what does ‘a’sin(x) mean?
the amplitude changes as there is a stretch in the y direction with a scale factor ‘a’; you would multiply each y-coordinate by ‘a’ (‘a’ times as high, ‘a’ times as low)
what does sin(‘a’x) mean?
the period changes as there is a stretch in the x direction with a scale factor 1/’a’: you would divide each x=coordinate by ‘a’ (everything happens ‘a’ times as fast)
what does sin(x)+a mean?
translation of ‘a’ units in the y-direction (+ up, - down)
what does sin(x-a) mean?
translation of ‘a’ units in x-direction (+ left, - right)
what does -sin(x) mean?
reflection in x-axis
what does sin(-x) mean?
reflection in y-axis
what does sin(x)= when x is less than 180?
sin (x) = sin (180 - x)
what does cos(x)= ?
cos (x) = cos (360 - x)
what does sin (x) = ?
sin (x) = cos (90 - x)
how do you find repeating solutions to a trig angle?
add 360 for cos and sin, and add 180 for tan
