Trigonometry Flashcards
Side lengths for 45 degree triangle
Hypotenuse = x√2
45 leg = x
Side lengths for 60-30 degree triangle
Hypotenuse = 2x
60 leg = x√3
30 leg = x
sin θ
opp / hyp
cos θ
adj / hyp
tan θ
opp / adj
csc θ
reciprocal of sine
hyp / opp
sec θ
reciprocal of cosine
hyp / adj
cot θ
reciprocal of tangent
adj / opp
sin 30
cos 60
cos 30
sin 60
tan 30
1 / tan 60 (reciprocals)
sin 45
cos 45
tan 45
1
Unit Circle, 30 degree Q1 coordinate
(√3 / 2, 1/2)
Unit Circle, 45 degree Q1 coordinate
(√2/2, √2/2)
Unit Circle, 60 degree Q1 coordinate
(1/2, √3 / 2)
Turning degrees to radians
degree divided by 180, include pi
degrees(pi/180)
Turning radians to degrees
multiply radians by 180, then divide number by denominator.
radians(180/pi)
Co-terminal angles
Angles in standard position with the same terminal side are co-terminal angles. (full 360 around both directions)
- if adding 360 does not result in positive answer, keep adding 360 and vise versa
2pi = 360
Reference angles
the positive angle formed on the x-axis.
- has to touch x-axis
- need to be in quadrant 1
Trig functions, sin θ
y coordinate
Trig functions, cos θ
x coordinate
Trig functions, tan θ
y / x
sin / cos
Q1 positive trig functions
ALL
Q2 positive trig functions
sin θ, csc θ
Q3 positive trig functions
tan θ, cot θ
Q4 positive trig functions
cos θ, sec θ
How to look at inverse trig functions
sin -1 (1/2)
ask, ‘where is y equal to. . .?’ to the 1/2
look at the sign as well
Quotient identities
tan θ = sin θ/cosθ
cot θ = cos θ/sin θ
Reciprocal identities
sin θ = 1/csc θ
cos θ = 1/sec θ
tan θ = 1/cot θ
the same with csc, sec, cot flipped postions
Pythagorean identities
cos^2 θ + sin^2 θ = 1
tan^2 θ +1 = sec^2 θ
cot^2 θ +1 = csc^2 θ
Helpful techniques for simplifying expressions
Change everything to sine or cosine
factoring to simplify expression if possible
get common denominators if there are fractions
multiply by conjugates
