# Solving Interval Equation: cosec^2x=(3cotx+4)/2

• essaichay
In summary, the conversation is about solving an equation and finding the values of x in a given interval. The speaker is confused about getting wrong answers when using a formula and asks for suggestions.
essaichay
Hi everyone,

Trying to revise and I came across this question:

Solve the eqn cosec^2x = (3cotx + 4)/2, giving all values of x in the interval 0 < x < 2pi in radians to two dp.

I ended up with two principal values/angles (working in degrees at the moment), which are:

tan^-1(x) = 26.6 deg. and tan^-1(x) = -63.4 deg.

i used the formula pv + 180n, and got the right answers for -63.4 deg, which are:

2.03 rad and 5.18 rad, but when I applied the same forumla to solve tan^-1(x) = 26.6 deg

I got one wrong answer to the mark scheme: 6.74 rad (supposed to be 0.46 rad) but one right answer: 3.61 rad.

Completely confused on this as I'm sure I didn't misuse the formula.

Any suggestions on this would be great!
Thanks in advance.

I think you are on the right track. The problem with 6.74 is that it doesn't fit in your interval. Keep in mind that you are dealing with radians and that 2 pi radians will take you all the way around the unit circle once. Try subtracting 2 pi from your answer (6.74) and look at what you get.

Last edited:

## 1. What is an interval equation?

An interval equation is an equation that involves variables within a specific range of values, known as an interval. This means that the equation only holds true for certain values of the variable.

## 2. How do I solve an interval equation?

To solve an interval equation, you need to isolate the variable on one side of the equation and keep the interval on the other side. Then, you can use algebraic techniques such as factoring, substitution, or the quadratic formula to find the values that satisfy the equation within the given interval.

## 3. What is cosecant and cotangent?

Cosecant (cosec) and cotangent (cot) are trigonometric functions that are the inverse of sine and tangent, respectively. Cosecant is equal to 1/sine, while cotangent is equal to 1/tangent. In other words, they represent the ratio of the hypotenuse to the opposite side and the adjacent side to the opposite side in a right triangle.

## 4. How do I apply the given equation to real-life problems?

The given equation can be applied in various real-life situations, such as calculating the angle of elevation or depression, determining the length of a side in a right triangle, or solving problems in physics and engineering that involve periodic functions.

## 5. What are the common mistakes to avoid while solving interval equations?

Some common mistakes to avoid while solving interval equations include forgetting to consider the interval, making calculation errors, and not checking the solutions in the original equation. It is also important to be familiar with the properties of trigonometric functions and basic algebraic rules.

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