Calculus of Trigonometric Functions?
1.dy/dx = sinx +xcosx = 0 all critical points occur when the derivative equals 0 so, sin = -xcosx divide by -cosx x = -tanx so, x + tanx = 0 2a. it helps to draw this out, and label on of the angles as x using trigonometry, we know that sinx = side1/ hyp, and that cosx = side2/hyp so, side1 = 15*sinx and side2 = 15cosx Perimeter = side1 + side2 + hyp =15sinx + 15cosx +15 = 15(sinx +cosx +1) b. simply take the derivative of the above formula for the perimeter dP/dt = 15cosx - 15sinx +0 dP/dt = 15(cosx -sinx) c. remember that critical points occur when the derived is equal to 0 so, 15(cosx -sinx) =0 cosx -sinx = 0 cosx = sinx the only time that sinx and cosx are equal is at pi/4 (from 0 to pi) thus, this is the only critical point
Write all the trigonometric functions in terms of sec x?
a) sinx = sqrt(sin^2x) = sqrt(1-cos^2x) = sqrt(1- 1/sec^2x) = sqrt[(sec^2x - 1)sec^2x] = sqrt(sec^2x - 1)/secx b) cosx = 1/secx c) tanx = sinx /cosx = sqrt(sec^2x - 1)/secx /1/secx = sqrt(sec^2x - 1) d) cotx = 1/tanx = 1/sqrt(sec^2x - 1) e) secx = secx f) csc x = 1/sinx = secx/sqrt(sec^2x - 1)
Solve trigonometric functions for solutions?
The first thing you want to do in just about any trig function like this is convert everything in terms of sin and cos. cotx = 1/tanx, but we know that tanx = sinx/cosx so cotx = cosx/sinx and cscx = 1/sinx, by definition. So what you really have is: cosx/sinx + 2/sinx = 3 Multiply both sides by sinx: cosx + 2 = 3 cosx = 1 x= arccos(1) x = 0 Since cos is only positive in the first and fourth quadrants, and this solution lies sort of in both of those, it is the only solution.
Which pair of trigonometric functions are both reciprocals and cofunctions?
tangent and cotanget
Do trigonometric functions only work for right triangles?
The general rules we study are like:Sin X = P/HCos X = B/HTan X = P/BThese are special cases when we fix one angle as 90 .The rules like Sine rule and Cosine rule works on all cases.Fixing one angle as 90 and other as Angle X will make the measures of angles as 90,X and 90-X and this makes it congruent with any other right angle triangle with angle X as one of the angle by AAA Theorem. By congruent properties the ratio of sides will always be fixed and defined.
Explicitly explain how ASTC helps to determine the signs (positive, negative) of trigonometric functions.?
explicitly explain how ASTC helps to determine the signs (positive, negative) of trigonometric functions. You should include all four quadrants, including the signs in each quadrant, and r.