Tan theeta+sec theeta =2/3 then tan
theeta- sec theeta =
Answers
Answer:
Step-by-step explanation:
For questions like this, involving transcendental functions, we usually have to use numerical methods to solve. (There are a few exceptions, when landmark points on the unit circle and trig identities get together in a nice way, but the numbers in this question don’t look like they would involve such fortunate circumstances.) Nowadays we can also solve problems like this with graphing calculators and graphing software, but these also use numerical methods to produce the graph.
To solve such a problem graphically, you’d get all the terms on one side and zero on the other, then put y=(whatever you got) in the calculator. Then you’d look for where your graph crosses the x axis, that’s where y=0, your solution.
When I put y=sec(theta) + tan(theta) - 2/3 into the online graphing calculator at symbolab.com, I saw that there are infinitely many solutions, spaced at intervals of 2pi, just as one would expect. According to that site, the principal solution is at 5.884, in the fourth quadrant. (We know it’s in the fourth quadrant because it’s between 3pi/2, approx 4.7, and 2 pi, approx 6.28.) This solution is in radians; the degree equivalent would be 337.12837 degrees. Both solutions are decimal approximations, as solutions to problems like this are usually irrational numbers.