# How do you solve ?

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.

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 .

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.

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

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