The Trigonometric functions are also called “
the circular functions” comprising trigonometry: the cosecant is called
cscx, cosine is called
cosx, cotangent is called
cotx, secant is called
secx, sine is called
sinx, and tangent is called
tanx in trigonometric functions
. However, their other notations are used occasionally. Their values with theta and functional values mentioned below:
Formulae:

Sin 2θ = 2 sin θ cos θ

Cos 2θ = cos²θ  sin²θ

cos²^{ θ}⁄_{2} = ^{(1+cosθ)}⁄_{2}

sin²^{ θ}⁄_{2} = ^{(1cosθ)}⁄_{2}
Example 1: Simplify 2 cosx cos2x sin3x – 2 sinx sin2x sin3x
(a) sin 4x (b) cos 4x (c) sin 6x (d) cos 6x
Answer: (c) sin 6x
Explanation: 2 cosx cos 2x sin 3x – 2 sinx sin 2x sin 3x
= 2 sin3x (cos x cos 2x – sin x sin 2x)
= 2 sin 3x (cos (x+2x))
= 2 sin 3x cos 3x
= sin 6x
Example 2: sec² x – 3sec x +2 = 0, 0 ≤ x ≤ 2π. Solve for x
Answer: Let sec x = y
y²  3y + 2 = 0
(y – 1) (y 2 ) = 0
y=1 or y = 2
sec x = 1 or sec x = 2
x = 0° or 60°