Math limit solver: Problem And Discussion Of Limit Of Trigonometric Functions

Math limit solver: Problem And Discussion Of Limit Of Trigonometric Functions.  The discussion and review of the Trigonometry of Mathematics is one of the Mathematical Formulas that deal with each other with the Corner of Triangle and Trigonometric Functions. As for the Trigonometry Formula itself is actually almost the same as Mathematical Geometric Formulas because both have a relationship and can be said that Trigonometry is part of Geometry so if you as students already understand about Trigonometry Mathematics it will not be difficult in understanding Geometry, so is the opposite.

Then the Basic Concept of Mathematical Trigonometry is the concept of the triangle of elbows and elbows and the corresponding sides of the two wakes come together which have the same comparisons. In the Euclid Geometry Concept each of the two corners of the Two Triangles has the same magnitude, the two Triangles must be concrete and this Concept is the basis for the comparison of Trigonometry Angle pointed, in which the concept of Trigonometry Mathematics has been developed again for Non pointed Angles or Angles that are over 90 degrees and less than ZERO degrees.

Then in the Trigonometric Mathematics has the first Three Functions is the Sinus which is the ratio of the Triangle Side (Triangle of Elbow or one of the Angle of Triangle is 90 °) which is in front of the angle with the Italic Side, then the second Trigonometric Function is Cosine or Cosine which is the side ratio The triangle which is located in the corner with the Lean Side and Basic Function of Third Math Trigonometry is Tangen which is comparison of Triangle Side which is in front of Angle with Triangle Side which is located in corner.

Limit of trigonometric function is part of the limit of trigonometric functions are quite complicated because it is a cross between limit and trigonometry the trigonometric concepts should also be so we understand. In fact, at the limit of trigonometric functions there are some patterns that can be used so it is not too difficult.

However, sometimes the problems about the limit of trigonometric functions becomes difficult because we have not mastered the concept of trigonometry. As a matter of the limit of other functions, sometimes we have to change the shape of the trigonometric functions becomes more simple to follow the pattern that has existed.

To the limit of trigonometric functions with x to zero we just need to memorize some of that value certainly based on the concept of a limit. Following some common patterns that we must understand:

lim         sin x  = 1
x → 0       x
lim            x   = 1                        
x → 0     sin x                       
lim            x    = 1                    
x → 0     tan x                          
lim          sin  ax   = 1
x → 0        bx
lim            ax        = 1      
x → 0      sin bx
lim         tan  ax    = 1
x → 0       bx

Formula of Amount and Difference of Trigonometry Angle

→  sin (A+B) = sinA cosB + cosA sinB
→ sin (A-B) = sinA cosB - cosA sinB
→  cos (A+B) = cosA cosB - sinA sinB
→ cos (A-B) = cosA cosB + sinA sinB
→ tan (A+B) = tanA + tanB
                    1 - tanA tanB

→ tan (A-B) =   tanA - tanB                 
                     1 + tanA tanB

Mathematical Trigonometry Multiplication Formulas

→ 2 sinA cosB = sin(A+B) + sin (A-B)
→ 2 cosA sinB = sin(A + B) - sin (A - B)
→ 2 cosA cosB = cos (a+B) + cos (A - B)
→ 2 sinA sinB = - cos (A + B) + cos (A - B)

Number and Trigonometry Difference Formulas

→ sinA + sinB = 2sin 1/2(A+B) cos 1/2 (A-B)
→ sinA - sinB = 2cos 1/2(A+B) sin 1/2 (A-B)
→ cosA + cosB = 2cos 1/2(A+B) cos 1/2 (A-B)
→ cosA - cosB = 2sin 1/2(A+B) sin 1/2 (A-B)

Duplex Angle and Three Trigonometry Formulas

→ sin2A = 2 sinA cosA
→ cos2A = cos²A - sin²A = 1 - 2sin²A = 2cos²A - 1
→ tan2A =   2 tanA    =    2 cotA         =            2         
                     1-tan²A       cot²A - 1            cotA - tanA

Exercises

Problem No.1

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Determine the following values
lim         sin 5x  
x → 0        15


Problem discussion

lim         sin 5x      =  5
 x → 0       15x          15

limit        sin 5x   =  1
x→ 0         15x         3

Problem No.2

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Determine the following values
lim            4x      
x → 0     tan 12x

Problem discussion

lim             3x      =  3
 x → 0     tan 12x     12

lim             4x      =  1
 x → 0     tan 12x     4

Problem No.3

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Determine the following values
lim        -3x + sin 2x
x → 0          6x

Problem discussion

lim        -3x + sin 2x
x → 0          6x 

lim        -3x  +  sin 2x       = -3  + 2
x → 0    6x          6x              6      6

lim        -3x + sin 2x     =  -1
x → 0          6x                   6

Probably just like that the discussion of Mathematical Trigonometry Formulas we have reviewed and write more fully, hopefully what we have written about the Basic Formulas of Mathematical Trigonometry can be understood easily by you and hopefully useful.