What is the Value of Cos 75°?

Answer. In trigonometry, we have faced a bunch of operators which are sine (sin), cosine (cos), tangent (tan), cosecant (cosec), secant (sec), and cotangent (cot).

Each of the operators has its own meaning and functions. The concept behind using the cosine (cos) operator is as follows.

Suppose a right-angled triangle has another angle valued θ. Considering θ, the cosine (cos) operator means:

cos θ = base/hypotenuse (base is considered as the length of the side of the triangle which is abiding by the angle θ)

For different values of θ, (cos θ) produces different values and for θ = 75° (or 5π/12 radian), the value cos75° will be,

cos75° =  cos (30° + 45°)

=cos30°×cos45° – sin30°×sin45° [by formula of cos(α+β)]

=(√3/2)×(1/√2) – (1/2)×(1/√2)

=( √3 -1)/2√2

= 0.2588190…