Article: Forgiveness is about accepting what has happened and moving forward. It is not a denial of the betrayal or a justification of what the other person did. It does not guarantee that the other person won’t hurt you again, but it can bring you a sense of power and peace.  You can choose not to forgive, but keep in mind that if you dwell on the broken trust, you might experience depression, anxiety, anger, and lack of connection with others.  You can forgive someone without reconciling or staying in the relationship. You can start the process of forgiveness by reflecting on how the experience of broken trust has affected you and your relationship to the other person. You can also reflect on the positive times in your relationship. What do you miss about your relationship and how would you like to get back to that?  If you get stuck: Consider the other person’s perspective and what you would want if you were in their position. Consider other times and experiences in life where your trust was broken or you broke someone’s trust. How were you able to forgive or were others able to forgive you? Consider journaling, talking to a friend or loved one, or talking to a counselor to help guide you. Instead of replaying and reliving the hurt feelings in your head, try to shift your focus to looking for healthy relationships and experiences that bring you happiness, hope, and peace.If you get overwhelmed in feeling the hurt while you’re trying to forgive, try practicing these techniques to ease your stress level:  Deep breathing Meditation Mindfulness exercises Forgiveness is not complete without reflecting on what you’ve learned. Use this experience to set boundaries and expectations in future relationships. Above all, trust yourself. If you’re unable to move on and completely forgive just yet, it might be too difficult to be around the person who broke your trust.
Question: What is a summary of what this article is about?
Understand what forgiveness is. Begin to forgive. Shift your emotions. Learn and move on.

Problem: Article: Suppose, as a different problem, that you know two sides and need to solve an unknown angle. You are given that side A is 10 inches long, side B is 7 inches long, and angle α{\displaystyle \alpha } is 50 degrees. You can use this information to find the measurement of angle β{\displaystyle \beta }. Set up the problem as follows:  Asin⁡α=Bsin⁡β{\displaystyle {\frac {A}{\sin \alpha }}={\frac {B}{\sin \beta }}} 10sin⁡50=7sin⁡β{\displaystyle {\frac {10}{\sin 50}}={\frac {7}{\sin \beta }}} sin⁡β=7sin⁡5010{\displaystyle \sin \beta ={\frac {7\sin 50}{10}}} sin⁡β=7∗0.76610{\displaystyle \sin \beta ={\frac {7*0.766}{10}}} sin⁡β=0.536{\displaystyle \sin \beta =0.536} In the above example, the law of sines provides the sine of the selected angle as its solution. To find the measure of the angle itself, you must use the inverse sine function. This is also called the arcsine. On a calculator, this is generally marked as sin−1{\displaystyle \sin ^{-1}}. Use this to find the measure of the angle. For the example above, the final step is as follows:  sin⁡β=0.536{\displaystyle \sin \beta =0.536} β=arcsin⁡0.536{\displaystyle \beta =\arcsin 0.536}  β=32.4{\displaystyle \beta =32.4}. Suppose you are told that angle α=30 degrees{\displaystyle \alpha =30{\text{ degrees}}}, angle β=50 degrees{\displaystyle \beta =50{\text{ degrees}}}, and side C, which connects them, is 10 inches long. Find the measurement of all sides and angles for the triangle.  First, you should recognize that you do not yet have enough information for the sine rule to apply. The sine rule requires that you have at least one pair with an angle that opposes a known side. However, you can calculate the third angle of this triangle using simple subtraction. All three angles add up to 180 degrees, so you can find angle γ{\displaystyle \gamma } by subtracting: γ=180−α−β=180−30−50=100{\displaystyle \gamma =180-\alpha -\beta =180-30-50=100}  Now that you know all three angles, you can use the sine rule to find the two remaining sides. Solve them one at a time:  Csin⁡γ=Bsin⁡β{\displaystyle {\frac {C}{\sin \gamma }}={\frac {B}{\sin \beta }}} 10sin⁡100=Bsin⁡50{\displaystyle {\frac {10}{\sin 100}}={\frac {B}{\sin 50}}} 10sin⁡50sin⁡100=B{\displaystyle {\frac {10\sin 50}{\sin 100}}=B} 10∗0.7660.985=B{\displaystyle {\frac {10*0.766}{0.985}}=B} 7.78=B{\displaystyle 7.78=B}   Thus, side B is 7.78 inches long. Now solve for the final remaining side.  Csin⁡γ=Asin⁡α{\displaystyle {\frac {C}{\sin \gamma }}={\frac {A}{\sin \alpha }}} 10sin⁡100=Asin⁡30{\displaystyle {\frac {10}{\sin 100}}={\frac {A}{\sin 30}}} 10sin⁡30sin⁡100=A{\displaystyle {\frac {10\sin 30}{\sin 100}}=A} 10∗0.50.985=A{\displaystyle {\frac {10*0.5}{0.985}}=A} 5.08=A{\displaystyle 5.08=A}   Side A, therefore, is 5.08 inches long. You now have all three angles, 30, 50 and 100 degrees, and all three sides, 5.08, 7.78, and 10 inches.
Summary: Solve for an unknown angle. Use the inverse function if needed to find the angle. Solve a problem with incomplete information.

To make a simple bubble solution, all you need is liquid dish soap, water, and glycerin. Dawn and Joy brands work best, but feel free to experiment with other detergents.  You can buy glycerin at craft stores or from a pharmacy.  You can use light corn syrup instead of glycerin. Mix 2/3 cup dish soap, 1 gallon (3.8 L) of water, and 2-3 tablespoons of glycerin for a basic bubble solution. Stir the ingredients together gently, taking care not to create too much foam.  It is best to keep your solution in a clean jar with a lid.  If you are replacing the glycerin with corn syrup, you will need to adjust your ratios. Use 1/4 cup of light corn syrup for each tablespoon of glycerin.  For best results, let the solution sit overnight. There are several different recipes for making bubble soap. The ratio of the ingredients will determine the strength of your bubbles. Soap helps the water to form a bubble by stabilizing the water molecules. Increasing the amount of soap in your solution may yield a stronger bubble. However, too much soap could cause the bubbles to collapse. Glycerin and corn syrup help create a "skin" for the bubbles, helping them last longer.
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Gather your ingredients. Make your solution. Experiment with other recipes.