if tan theta=1.0024 find an approximate value of theta
Answers
Answer:If theta satisfy (-90<= theta <= 90), then theta = arctan(4/3). This is approximately 53.13 degrees.
The set of all theta satisfying tan(theta) = 4/3 is the previous value plus or minus a multiple of Pi (which corresponds to 180 degrees). This set is {53.13 + k * 180, where k is an arbitrary integer}.
An interesting note is when we consider this theta in the context of a right angle triangle. If so, angle theta will correspond to the acute angle that opposes the altitude of 4 and a base of 3 (in fact their length may be positive multiples of these numbers). By using the well known Pythagorean Theorem, we get the hypotenuse to be 5. This is the famous fundamental right angle triangle of sides 3, 4, 5. Despite that, this is not necessarily very helpful to find theta. Instead we can easily find the other trigonometric functions, such as sin(theta) = 4/5, cos(theta) = 3/5, and so on. Again, this would be probable a good question for high school tests, like this: "Given theta an acute angle in a right angle triangle such that tan(theta) is 4/3, find sin(theta)." There are many methods to solving it, but perhaps the most interesting one is to use the famous (3, 4, 5) right angle triangle.
Step-by-step explanation: