sin 120 Y8 cos 120 tan 120 V3 sin 120 cos 120 tan 120 ” 2 V3
The Correct Answer and Explanation is:
The correct values for the trigonometric functions of 120 degrees are:
sin 120° = √3/2 cos 120° = -1/2 tan 120° = -√3
These values can be derived using the unit circle and reference angles. In trigonometry, the sine, cosine, and tangent functions are defined based on the ratios of the sides of a right triangle. When dealing with angles greater than 90 degrees, reference angles and quadrant signs must be considered.
120 degrees falls in the second quadrant of the unit circle. The reference angle for 120 degrees is found by subtracting it from 180 degrees, which gives 60 degrees. The sine function remains positive in the second quadrant, while the cosine and tangent functions are negative.
Since the reference angle is 60 degrees, we use the known trigonometric values of 60 degrees:
sin 60° = √3/2 cos 60° = 1/2 tan 60° = √3
To determine the values at 120 degrees:
sin 120° retains the same value as sin 60°, so it remains √3/2. cos 120° is the negative of cos 60°, resulting in -1/2. tan 120° is the negative of tan 60°, yielding -√3.
These results align with the general behavior of trigonometric functions in different quadrants. The unit circle provides a structured way to evaluate sine, cosine, and tangent for various angles, ensuring accuracy in calculations. Understanding this framework is essential for solving problems in physics, engineering, and applied mathematics.
