Determine the signs of the trigonometric functions of an angle in standard position with the given measure. See Example 2. ―345°

Key Concepts

Standard Position of an Angle

An angle is in standard position when its vertex is at the origin of a coordinate system and its initial side lies along the positive x-axis. The angle is measured counterclockwise from the initial side. If the angle exceeds 360°, it wraps around, and negative angles are measured clockwise. Understanding this positioning is crucial for determining the signs of trigonometric functions.

Unit Circle

The unit circle is a circle with a radius of one centered at the origin of a coordinate plane. It is fundamental in trigonometry as it provides a geometric representation of the sine, cosine, and tangent functions. The coordinates of points on the unit circle correspond to the cosine and sine values of the angle, which helps in determining the signs of these functions based on the quadrant in which the angle lies.

Signs of Trigonometric Functions in Quadrants

The signs of trigonometric functions vary depending on the quadrant in which the terminal side of the angle lies. In the first quadrant, all functions are positive; in the second, sine is positive; in the third, tangent is positive; and in the fourth, cosine is positive. For an angle of -345°, which is equivalent to 15° in the first quadrant, both sine and cosine are positive, while tangent is also positive.