Definition of the sine and cosine of an angle x
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samalbee
<p>The definitions of the sine, cosine, tangent and cotangent functions can now be formulated for any circle or for the unit circle (i.e. a circle with radius r = 1 unit of length).</p>
<p>With respect to the unit circle - <a href="https://domyhomework.club/">do my homework for money</a> , the following definitions (equivalent to the definitions on any circle) apply:</p>
<p>The ordinate v of the point belonging to the angle x</p>
<p>P(u; v) on the unit circle is called sine of the angle x:</p>
<p>sin x= (average)PQ/(average)OP=v/1=v (x∈[0; 2π]).</p>
<p>The abscissa u of the point P belonging to the angle x on the unit circle is called cosine of the angle x:</p>
<p>cos x=(average)OQ/(average)OP=u/1=u (x∈[0; 2π])</p>
<p>The unique assignment x→sin x is called the sine function, and the unique assignment x→cos x is called the cosine function accordingly.</p>
<p>If we assume that the second leg of the angle x can be rotated around the origin as often as desired and, moreover, in the mathematically positive as well as in the mathematically negative sense of rotation - <a href="https://domyhomework.club/math-problem-solver/">https://domyhomework.club/math-problem-solver/</a> , the concept of angle can be extended:</p>
<p>Each additional full rotation increases the angle by 2π or 360° (for counterclockwise rotation) or -2π or -360° (for clockwise rotation).</p>
<p>Thus, the entire set R of real numbers can be used as the domain of definition of the sine and cosine functions.</p>
<p><strong>Thus, for example, it is valid:</strong></p>
<p>The definition of the tangent of an angle x can be done immediately using the sine and cosine of this angle - <a href="https://domyhomework.club/microeconomics-homework/">microeconomics homework help</a> , but also with reference to the unit circle and the tangent to it at the point (1; 0).</p>
<p>For any angle x (x∈R and x ≠ (2k+1)π/2, k∈Z), the quotient of the sine and cosine of this angle is called the tangent of the angle x.</p>
<p>The unique assignment x→ tan x is called the tangent function.</p>
<p>Correspondingly, the quotient of the cosine and the sine of an angle x (x∈R and x≠k π, k∈Z) is called the cotangent of x and the unique assignment x→ cot x is called the cotangent function.</p>
<p>Sine, cosine, tangent and cotangent functions are special angle functions or trigonometric functions.</p>
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2 years, 4 months ago
