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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.
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. By symmetry, the bisected side is half of the side of the equilateral triangle, so one concludes sin ( 30 ∘ ) = 1 / 2 {\displaystyle \sin(30^{\circ ...
Tripotassium phosphate, also called tribasic potassium phosphate [3] is a water-soluble salt with the chemical formula K 3 PO 4. (H 2 O) x (x = 0, 3, 7, 9). [ 4 ] Tripotassium phosphate is basic: a 1% aqueous solution has a pH of 11.8.
Similar right triangles illustrating the tangent and secant trigonometric functions Trigonometric functions and their reciprocals on the unit circle. The Pythagorean theorem applied to the blue triangle shows the identity 1 + cot 2 θ = csc 2 θ, and applied to the red triangle shows that 1 + tan 2 θ = sec 2 θ.
Potassium phosphate is a generic term for the salts of potassium and phosphate ions including: [1] Monopotassium phosphate (KH 2 PO 4) (Molar mass approx: 136 g/mol) Dipotassium phosphate (K 2 HPO 4) (Molar mass approx: 174 g/mol) Tripotassium phosphate (K 3 PO 4) (Molar mass approx: 212.27 g/mol) As food additives, potassium phosphates have ...
Likewise, tripolyphosphoric acid H 5 P 3 O 10 yields at least five anions [H 5−k P 3 O 10] k−, where k ranges from 1 to 5, including tripolyphosphate [P 3 O 10] 5−. Tetrapolyphosphoric acid H 6 P 4 O 13 yields at least six anions, including tetrapolyphosphate [P 4 O 13] 6−, and so on. Note that each extra phosphoric unit adds one extra ...
Signs of trigonometric functions in each quadrant. All Students Take Calculus is a mnemonic for the sign of each trigonometric functions in each quadrant of the plane. The letters ASTC signify which of the trigonometric functions are positive, starting in the top right 1st quadrant and moving counterclockwise through quadrants 2 to 4.
Substance Formula 0 °C 10 °C 20 °C 30 °C 40 °C 50 °C 60 °C 70 °C 80 °C 90 °C 100 °C Barium acetate: Ba(C 2 H 3 O 2) 2: 58.8: 62: 72: 75: 78.5: 77: 75