Solving a Physics Problem: Sine vs. Cosine Theta

In summary, sine and cosine theta are two trigonometric functions commonly used in physics to solve problems involving angles and distances. Sine theta represents the ratio of the opposite side to the hypotenuse in a right triangle, while cosine theta represents the ratio of the adjacent side to the hypotenuse. The choice between sine and cosine theta depends on the given information in the problem, with sine being used for opposite and hypotenuse sides and cosine for adjacent and hypotenuse sides. The value for sine or cosine theta can be found using a calculator or trigonometric table, with the angle measure in degrees or radians being essential. The process for solving a physics problem using these functions involves identifying the appropriate function, finding the value of sine
  • #1
Faiq
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Homework Statement


Question is provided

The Attempt at a Solution


The required solution is provided

My question is, the examiner have used sine theta in their expression for change in potential. I keep ending up with 1 - cosine theta
Second question is how did they get rid of theta in the proceeding equation
 

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  • #2
See the left side. For small angles, ##\sin \theta \approx \theta## and ##\cos \theta \approx 1 - \frac 1 2 \theta^2## (sometimes ##\cos \theta \approx 1## is sufficient).
 
1.

What is the difference between sine and cosine theta in solving a physics problem?

Sine and cosine theta are both trigonometric functions used in physics to solve problems involving angles and distances. Sine theta represents the ratio of the opposite side to the hypotenuse in a right triangle, while cosine theta represents the ratio of the adjacent side to the hypotenuse.

2.

When should I use sine theta and when should I use cosine theta in a physics problem?

The choice between sine and cosine theta depends on the given information in the problem. If the problem involves the opposite and hypotenuse sides of a triangle, you should use sine theta. If the problem involves the adjacent and hypotenuse sides, you should use cosine theta.

3.

How do I know which value to use for sine or cosine theta in a physics problem?

The value for sine or cosine theta can be found using a calculator or trigonometric table. You will need to know the measure of the angle in degrees or radians to find the correct value.

4.

What is the process for solving a physics problem using sine and cosine theta?

The first step is to identify which trigonometric function to use based on the given information. Then, use a calculator or table to find the value of sine or cosine theta. Finally, substitute the values into the appropriate formula and solve for the unknown variable.

5.

Are there any common mistakes to avoid when using sine and cosine theta to solve a physics problem?

One common mistake is using the incorrect value for theta. Make sure to use the correct measure of the angle, either in degrees or radians, when finding the value of sine or cosine theta. Additionally, be careful when substituting the values into the formula to avoid errors in calculation.

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