Solving Trigonometic Equations
solve for x : ( by radian)
1)cotx= 3
2)secx = 0.5
<<<and thanks >>>
1) Same as tan x = 1/3. Use a calculator. I get 0.321 radians
2) sec x = 0.5 is not possible. The absolute value of the secant must be one or more.
<< Thanks drwls for your help >>
To solve the trigonometric equation cot(x) = 3, you need to find the value of x in radians. Here's how you can do it:
Step 1: Rewrite the equation as tan(x) = 1/3. Since cot(x) is the reciprocal of tan(x), we can rewrite the equation to use tan(x) instead.
Step 2: Use a scientific calculator or a trigonometric table to find the inverse tangent (or arctan) of 1/3. This will give you the value of x in radians.
For example, using a calculator, you would press the "2nd" or "shift" button and then the "tan" or "tan^(-1)" button followed by inputting 1/3. The result for x in radians is approximately 0.321.
Therefore, the solution to the equation cot(x) = 3 (in radians) is x = 0.321.
Regarding the equation sec(x) = 0.5, there is no solution in radians. The secant function represents the reciprocal of the cosine function, and cosine values can only be between -1 and 1. Since the absolute value of the secant must be greater than or equal to one, there is no value of x that satisfies the equation sec(x) = 0.5.