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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