Angles and Measurement – Complete Grade 11 Maths Unit | Radians, Arc Length, Sector Area, Worksheets & Assessment

Trigonometric functions of any angles

Let θ be the measure angle AOB in standard position.

Let P (x,y) be any point on the terminal arm OB such that l(OP) = r

The trigonometric functions of angle θ as follows


B y r
y s in   co sec  
P(x,y) r y

θ
A x r
cos   sec  
r x
x’ O x

y x
tan   cot  
x y
y’

, Trigonometric functions with the help of standard unit circle
Let P ( x , y ) be any point on the unit circle with m∠XOP = θ . Since P lies on
the unit circle .

l(OP)= 1 √ x2 + y 2 = 1 Y
, y)
∴x +y =1
2 2 (x
P
Then we define the trigonometric function
as follows
1 1 θ
sin   y cos ec    , y 0
sin  y
M O X

1 1
cos   x sec    , x 0
cos  x

sin y cos  x
tan   , x 0 cot    , y 0
cos x sin  y