If [tex]cos 30^{\circ} =\frac{\sqrt{3}}{2}[/tex] and [tex]tan 15 = 2-\sqrt{3}[/tex]
Answer (2)
The two trigonometric values given are cos 3 0 ∘ = 2 3 and tan 1 5 ∘ = 2 − 3 . These values are essential in various applications in mathematics, physics, and engineering, where angles and distances need to be calculated. They help solve problems related to projectile motion and the design of structures.
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The question provides two trigonometric values: cos 3 0 ∘ = 2 3 and tan 1 5 ∘ = 2 − 3 . These values are exact and can be used in various trigonometric calculations and applications. There is no specific problem to solve, but the values are provided as given information. Given values: cos 3 0 ∘ = 2 3 , tan 1 5 ∘ = 2 − 3
Explanation
Examples
The given trigonometric values can be used in various fields like physics (calculating angles of projectile motion), engineering (designing structures), and navigation (determining directions and distances). For example, in physics, if you're analyzing the trajectory of a projectile launched at an angle of 30 degrees, knowing the cosine of 30 degrees helps determine the horizontal component of the initial velocity. Similarly, the tangent of 15 degrees can be useful in calculating the slope of a ramp or incline in engineering applications. These trigonometric values are fundamental in solving problems involving angles and distances in two-dimensional space.
