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The values of sine and cosine of 30 and 60 degrees are derived by analysis of the equilateral triangle. In an equilateral triangle, the 3 angles are equal and sum to 180°, therefore each corner angle is 60°. Bisecting one corner, the special right triangle with angles 30-60-90 is obtained.
In mathematics, sine and cosine are trigonometric functions of an angle.The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that ...
Ptolemy's theorem states that the sum of the products of the lengths of opposite sides is equal to the product of the lengths of the diagonals. When those side-lengths are expressed in terms of the sin and cos values shown in the figure above, this yields the angle sum trigonometric identity for sine: sin(α + β) = sin α cos β + cos α sin β.
For example, the cosine and sine of 2π ⋅ 5/37 are the real and imaginary parts, respectively, of the 5th power of the 37th root of unity cos(2π/37) + sin(2π/37)i, which is a root of the degree-37 polynomial x 37 − 1.
The y-axis ordinates of A, B and D are sin θ, tan θ and csc θ, respectively, while the x-axis abscissas of A, C and E are cos θ, cot θ and sec θ, respectively. Signs of trigonometric functions in each quadrant. Mnemonics like "all students take calculus" indicates when sine, cosine, and tangent are positive from quadrants I to IV. [8]
Trigonometric ratios can also be represented using the unit circle, which is the circle of radius 1 centered at the origin in the plane. [37] In this setting, the terminal side of an angle A placed in standard position will intersect the unit circle in a point (x,y), where x = cos A {\displaystyle x=\cos A} and y = sin A {\displaystyle ...
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The degree Celsius is the unit of temperature on the Celsius temperature scale [1] ... 37.0 °C 98.6 °F 558.27 °R Boiling point of water [b] 373.1339 K