# 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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