How To Do Trigonometry How To Do Trigonometry
Trigonometric functions, has wide application in Differential Calculus, firstly we will see how to do trigonometry in calculus? When we deal with trigonometry we have to deal with different types of formulas. The differentiation of trigonometric function is given below: 1: d/dx(sinx) = cosx 3: d/dx(tanx ) = sec2x 5: d/dx(cosecx)=-cosecx *cotx
2: d/dx(cosx)= -sinx 4: d/dx(secx)=secx*tanx 6: d/dx(cotx)= -cosec2x
As you can see that the trigonometric functions having co in front of their name always have minus sign in front of there the differential. Now, see one example for understanding the concept properly. Example 1: Differentiate the given function with respect to x, when y= sinx +2cosx? Solution: d/dx(y) = d/dx(sinx +2cosx) For this type of case, we need to differentiate both the function separately than, after differentiation we can add them. Know More About Differentiation Formulas
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dy/dx= d/dx(sinx) + d/dx(2cosx), dy/dx = cosx +(-2sinx), dy/dx=cosx-2sinx. This is the required answer. Example 2: Differentiate with respect to x, when y=tanx *secx? Solution: For solving this type of problem we need to apply product rule, when we apply product rule we get solution as follows: d/dx(y)= tanx *d/dx(secx) + secx * d/dx(tanx), dy/dx = sec2x*secx *tanx + secx *sec2x, dy/dx= sec3xtanx + sec3x, Now, taking sec3x as common we will get: dy/dx = sec3x(tanx +1), This is the final solution of the problem. Example 3: Differentiate with respect to x, when Y= sec3x? Solution: Now we only know the differential of secx so, we need to write secx three times so that we can differentiate it easily. There are three functions and we can’t apply product rule, for product rule we need two functions, we can apply product rule by taking two functions at a time but it becomes complicated so we will follow the technique given below: sec3x = secx*secx*secx, Y= secx*secx*secx, d/dx(y)= d/dx(secx*secx*secx), We can differentiate the function as: dy/dx = d/dx(secx)secx*secx + secx *d/dx(secx)*secx + secx *secx* d/dx(secx), now as we know secx can be differentiate as secx * tanx dy/dx = secx*tanx(sec2x) + sec2x(secx*tanx) + secx*tanx(sec2x) Now this big equation can be written as: dy/dx = 3secx*tanx (sec2x), In this way, you can differentiate the trigonometric function in calculus. Trigonometry is that branch of mathematics which deals with the real life problems related to angles. Read More About Rational Numbers Examples
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Trigo means three sides, so trigonometry is basically a branch of mathematics which relates to the study of three sided figures i.e. triangles, their sides and the angles between them. In trigonometry we take into consideration a right angle triangle with acute angles. These relations are used to solve real life problems related to inclination at a particular point. Trigonometry is used to find the angles or the distance between the two points when the angle of inclination is known. We take into consideration only those triangles in trigonometry where we have a right angled triangle. The most familiar functions of trigonometry are sin, cos and tan. The study of trigonometry mainly revolves around these three functions. Some basic formulas used in trigonometry called trigonometric ratios are you must be familiar with all these formulas in order to solve different trigonometric problems. Here, is the list of trigonometric formulas which are commonly used to represent the trigonometric ratios.
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Thank You
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