How do you solve ?

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Answer


Qian

Solution:

 

Step:1 Trigonometry ratio is defined as the ratio for perpendicular to the base of right angled triangle with respect to the angle .

 

Consider the right triangle  such that right angled at  as shown in Figure 1.

 

 

Step:2 As it is given that  is equal to the fraction . Compare the fraction with corresponding side ratio of perpendicular  and base .

 

 

 

From the above comparison, it can be assumed that side perpendicular of the triangle is  and base is .

 

Use the Pythagoras theorem to calculate the third side (hypotenuse) of the right triangle whose perpendicular is  and base is .

 

 

Step:3 Pythagoras theorem states that square of hypotenuse is equal to the sum of square of the perbendicular and the square of the base.

 

 

Further, solve the above equation as follws:

 

 

Take the square root on both sides and obtain the length of hypotenuse  as .

 

Step:4  Therefore, the equation of is equivalent to the equation  or  for the first quadran or in a angle from 0 to 90 degree.

 

Step:5 Now, to find the value of  in the equation  is equivalent to find the value of  in the equation .

 

 

The function  or  is the inverse function of

 

Now use the calculator to find the value of  as shown below:

 

 

Thus, the value for  is 26.56505118 degree.

 

Step:6 Simillarly, the equation  is equaivalent to  and use calculator to obtain the value of x.

 

 

Therefore, the principle solution of the equation is 26.56505118 degree approximately.

 

Answer:

 

The principle solution of the equation  is 26.56505118 approximately.

 

 

Similar Problems:

 

Problem 1:

 

How do you solve  ?

 

Solution:

 

Step:1 Consider the equation .

 

Step:2 Compare both sides and obtain the value of x.

 

Principal value of  is .

 

Answer:

 

The solution of the equation  in principal region is .

 

 

Problem 2:

 

How do you solve  ?

 

Solution:

 

Step:1 Consider the equation .

Step:2 The equation  is equaivalent to  and use calculator to obtain the value of x.

 

 

Step:3 Therefore, the principle solution of the equation  is 35.26438968 degree approximately.

 

Answer:

 

The solution of the equation  in principal region is 35.26438968 degree approximately.

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