# Trigonometry Question: Dealing with Negative and Positive Values for Theta

• Samurai44
In summary, in trigonometry equation (finding theta):1) If the range of theta includes negative and positive part (such as -360<=theta<=360), and I got a value of 90,180,270 or 360.. do I have to write the answer twice positive and negative? No.2) if range of theta is positive only, and I got a negative value of theta, do I have to do 360 + (negative value of theta)? Yes.
Samurai44
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In trigonometry equation (finding theta):
1) If the range of theta includes negative and positive part (such as -360<=theta<=360), and I got a value of 90,180,270 or 360.. Do I have to write the answer twice positive and negative?

2) if range of theta is positive only, and I got a negative value of theta, do I have to do 360 + (negative value of theta)? .. To make the answer positive

1) no, all ##\theta## are in range (but see comment (*))
2. yes, repeatedly if necessary (you may find ##\theta## = -3000) -- the wording here is confusing: -120 would have to be reported as -120 + 360 = 240.

(*)
Make a drawing of the unit circle. ##-360 \le \theta\le +360## seems unlogical. Could it be ##-180 < \theta \le 180 ## ?

BvU said:
1) no, all ##\theta## are in range (but see comment (*))

(*)
Make a drawing of the unit circle. ##-360 \le \theta\le +360## seems unlogical. Could it be ##-180 < \theta \le 180 ## ?
But suppose the range is -180<=theta<=180
If i got a value of 90 or 180, would it be + and negative?

For the -360<=theta<=360 it's like two ranges : one is from 0 to 360, the other from 0 to -360, so two drawings.. Or maybe I have to write -360<=2theta<=360

But suppose the range is -180<=theta<=180
If i got a value of 90 or 180, would it be + and negative?
The 90 is positive and 90 - 360 is out of range. So +90 only.
The 180 is on the bound. Your bounds coincide, so both -180 and +180 are in range. But there is only one answer, so the overlapping bounds are not a good idea. That's why I used ##-180 < \theta \le 180##.

BvU said:
The 90 is positive and 90 - 360 is out of range. So +90 only.
The 180 is on the bound. Your bounds coincide, so both -180 and +180 are in range. But there is only one answer, so the overlapping bounds are not a good idea. That's why I used ##-180 < \theta \le 180##.
But consider this graph, isn't it possible to write -90?

In your case 1) the 270 is in range.
In your case 2) the 90 is in range and remains 90. The 270 is over range and comes in range by subtracting 360. In that sense -90 is one of the answers.

If i got a value of 90 or 180, would it be + and negative?
Perhaps I read this question in your post #3 in a different way than you intended.

To summarize:
case 1) 0, 90, 180, 270
case 2) 0, 90, 180, -90​

## 1. What is trigonometry?

Trigonometry is a branch of mathematics that deals with the study of triangles and their properties, specifically the relationships between their sides and angles. It is used to solve problems involving angles, distances, and heights in various real-world situations.

## 2. What are the three basic trigonometric functions?

The three basic trigonometric functions are sine, cosine, and tangent. These functions are used to relate the angles of a right triangle to the lengths of its sides.

## 3. How do you find the value of a trigonometric function?

The value of a trigonometric function can be found using a calculator or by using a table of values. These functions can also be evaluated using the unit circle or by using the Pythagorean theorem.

## 4. What is the difference between sine, cosine, and tangent?

Sine, cosine, and tangent are all trigonometric functions, but they differ in how they relate angles to sides of a triangle. Sine is the ratio of the opposite side to the hypotenuse, cosine is the ratio of the adjacent side to the hypotenuse, and tangent is the ratio of the opposite side to the adjacent side.

## 5. How is trigonometry used in real life?

Trigonometry is used in a variety of fields, including engineering, physics, and navigation. It is used to design buildings and structures, calculate distances and heights, and create maps and charts. It is also used in astronomy to study celestial objects and their movements.

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