sin A = -x/y
Since the sine is the ratio of the opposite leg to the hypotenuse, let's assume the opposite leg's length is -x and the hypotenuse's length is y. Let's call the adjacent leg's length z. So:
(-x)2+z2=y2
z2=y2-(-x)2
z2=y2-x2
z=√(y2-x2)
cos A = z/y = √(y2-x2)/y
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CosecA + CotA = 11/2Cosec2A - Cot2A = 1 {By the Identity}(CosecA + CotA) (CosecA - CotA) = 111/2 (CosecA - CotA) = 1(1/SinA) - (CosA/SinA) =2/11(1 - CosA) / SinA = 2/11Therefore 1 - CosA = 2CosA = 3 and SinA = 11Therefore TanA = SinA / CosA = 11/3
that cannot be proved because it is not necessarily true.
This is known as the Cosine Rule.
sin75 = sin(45 + 30) = sin45cos30 + cos45sin30 = (1/root 2)((root 3)/2) + (1/root 2)(1/2)
You'll have to work out the length of the third side using:a) the sine rule (if information given has one side opposite a given angle and the unknown side also opposite a given angle)SIN RULE: sinA/a = sinB/b = sinC/cb) the cos rule (not opposite).COSINE RULE: a2 = b2 +c2 -2bc x CosA