CovariantsDate: 05/02/97 at 11:09:14 From: Vincent Subject: Trigonometry Dr. Math, Please help me answer the following trigonometry problem: Express tan(pi/2 + X) as a single function of X or as a constant. Date: 05/02/97 at 11:45:34 From: Doctor Wilkinson Subject: Re: Trigonometry This problem involves the relations between the various trig functions and the "co" variants. For example, sine and cosine, tangent and cotangent, secant and cosecant. The "co" here relates to complementary angles. The sine of an angle is the cosine of the complement of the angle, and so on. So we have the formulas: sin(pi/2 - x) = cos(x) tan(pi/2 - x) = cot(x) sec(pi/2 - x) = csc(x) In your example, you have: tan(pi/2 + X) We can apply the second formula with x = -X to get: tan(pi/2 + X) = cot(-X) Now we are close. The cot(-X) = -cot(X). Remember the cotangent is the quotient of the sine and the cosine, and we have the formulas: sin(-x) = -sin(x) cos(-x) = cos(x) So cot(-x) = cos(x)/(-sin(x)) = -cos(x)/sin(x) = -cot(x) -Doctor Wilkinson, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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