<P> The most familiar trigonometric functions are the sine , cosine , and tangent . In the context of the standard unit circle ( a circle with radius 1 unit ) , where a triangle is formed by a ray starting at the origin and making some angle with the x-axis , the sine of the angle gives the length of the y - component ( the opposite to the angle or the rise ) of the triangle , the cosine gives the length of the x-component ( the adjacent of the angle or the run ) , and the tangent function gives the slope ( y - component divided by the x-component ) . More precise definitions are detailed below . Trigonometric functions are commonly defined as ratios of two sides of a right triangle containing the angle , and can equivalently be defined as the lengths of various line segments from a unit circle . More modern definitions express them as infinite series or as solutions of certain differential equations , allowing their extension to arbitrary positive and negative values and even to complex numbers . </P>
<P> The most familiar trigonometric functions are the sine , cosine , and tangent . In the context of the standard unit circle ( a circle with radius 1 unit ) , where a triangle is formed by a ray starting at the origin and making some angle with the x-axis , the sine of the angle gives the length of the y - component ( the opposite to the angle or the rise ) of the triangle , the cosine gives the length of the x-component ( the adjacent of the angle or the run ) , and the tangent function gives the slope ( y - component divided by the x-component ) . More precise definitions are detailed below . Trigonometric functions are commonly defined as ratios of two sides of a right triangle containing the angle , and can equivalently be defined as the lengths of various line segments from a unit circle . More modern definitions express them as infinite series or as solutions of certain differential equations , allowing their extension to arbitrary positive and negative values and even to complex numbers . </P>
what is tan in terms of sin and cos
what is tan in terms of sin and cos
gives the slope ( y - component divided by the x-component )
gives the slope ( y - component divided by the x-component )