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7
...
Let θ∈R
...
Let P(x, y) be a point on the
terminal side of the angle θ such that OP = r( > 0)
...
r
ii)
x
is called
r
iii)
y
x
iv)
x
(y ≠ 0) is called cotangent of θ and it is
y
v)
r
(x ≠ 0) is called secant of θ and it is denoted by secθ
...
denoted by cotθ
...
These six functions (ratios) are called trigonometric functions (ratios)
...
sinθ
...
cosθ
...
tanθ
...
sin θ
cosθ
= tan θ,
= cot θ
cos θ
sinθ
6
...
1+tan2θ= sec2θ, tan2θ = sec2θ − 1, sec2θ − tan2θ=1
...
1 + cot2 θ = cosec2 θ, cot2 θ = cosec2 θ −1,
cosec2 θ − cot2 θ = 1
...
sec θ + tan θ =
1
...
cosec θ + cot θ =
1
...
The values of the trigonometric functions of some standard angles :
θ
0
π/6
π/4
sin
0
1/2
1/
2
3
cos
1
3
1/
2
1/2
/2
π/3
/2
π/2
π
3π/2
2π
1
0
−1
0
0
−1
0
1
12
...
Trigonometric functions of (−θ), for all values of θ
1) sin(−θ) = −sin θ,
2) cos(−θ) = cos θ,
3) tan(−θ) = −tan θ,
4) cot(−θ) = −cot θ,
5) sec(−θ) = sec θ,
6) cosec(−θ) = −cosec θ
14
...
± θ where n∈Z, 0 ≤ θ ≤
π
2
i) sin⎛⎜ n
...
Then
= ± sin θ, if n is even
⎠
= ± cos θ, if n is odd
ii) cos ⎛⎜ n
...
± θ ⎞⎟ = ± tan θ, if n is even
⎝
⎠
= ± cot θ, if n is odd
iv) cot ⎛⎜ n
...
± θ ⎞⎟
⎝
= ± sec θ, if n is even
⎠
= ± cosec θ, if n is odd
π
2
vi) cosec ⎛⎜ n