Final answer:
The sine, cosine, and tangent values are determined for major angles using the unit circle or right triangle ratio methods and are foundational to trigonometry.
Step-by-step explanation:
The values of sin(x), cos(x), and tan(x) at major angles such as 0, π/6, π/4, π/3, π/2, π, and so on, are essential in trigonometry and can be derived from the unit circle or using right triangle relationships. For example:
sin(0) = 0 and cos(0) = 1, which implies that tan(0) = sin(0)/cos(0) = 0.
At π/6, sin(π/6) = 1/2 and cos(π/6) = √3/2, leading to tan(π/6) = 1/√3.
At π/4, both sin(π/4) and cos(π/4) are √2/2, which makes tan(π/4) = 1.
sin(π/3) = √3/2 and cos(π/3) = 1/2, thus tan(π/3) = √3.
For π/2, sin(π/2) = 1 and cos(π/2) = 0, which means tan(π/2) is undefined.
By continuing with this approach, you can find the values for all other major angles. These functions help in solving problems related to waves, oscillations, and triangles.