In a right triangle...
Hypotenuse - is the side opposite the right angle
Opposite - is the side across from the angle θ (theta)
Adjacent - is the side next to θ
Greek Letters --> represent angles
θ --> "Theta"
α --> "Alpha"
β --> "Beta"
3 Basic Trig. Functions
SohCahToa
Sine function: sin θ = length of the side opposite θ
length of the hypotenuse
Cosine function: cos θ = length of the side adjacent to θ
length of the hypotenuse
Tangent function: tan θ = length of the side opposite θ
length of te side adjacent to θ
Sin θ = y
z
Cos θ = x
z
Tan θ = y
x
3 Auxiliary Trig. Functions
The cosecant, secant, and cotangent functions are the respective reciprocals of the sine, cosine, and tangent functions.
csc θ = 1 = length of the hypotenuse
sin θ length of the side opposite θ
sec θ = 1 = length of the hypotenuse
cos θ length of the side adjacent to θ
cot θ = 1 = length of the side adjacent to θ
tan θ length of the side opposite θ
Csc θ = z
y
Sec θ = z
x
Cot θ = x
y
Pythagorean Theorem
--> In any right triangle a² + b² = c², where "a" and "b" are the legs and "c" is the length of the hypotenuse.
Exact Values
30° 45° 60°
Sin 1/2 √2/2 √3/2
Cos √3/2 √2/2 1/2
Tan √3/3 1 √3
Csc 2 √2 2√3/3
Sec 2√3/3 √2 2
Cot √3 1 √3/3
Angle of Elevation
- angle made from the horizon going up
Angle of Depression
- angle made from the horizon going down
Reference angles around the circle
Positive rotation
- counter clockwise
Negative rotation
- clockwise
Initial side --> where angle starts
Terminal side --> where angle ends
Standard Position --> the initial side is the positive x-axis every time.
Positive Quadrants
Reference Angle --> a positive, acute angle made from the terminal side of any angle to the x-axis.