Radians: A Valuable Alternative Angle Measurement in Trigonometry

When it comes to solving equations in trigonometry, we often rely on degrees as our go-to angle unit. However, there is another unit that can be more useful when dealing with circles - radians. Let's take a closer look at what radians are and how they can be applied in trigonometry problems.

What Exactly are Radians?

Radians are an alternative unit of measurement used in solving trigonometric equations. To better understand their concept, let's visualize a circle with a radius of 1 unit.

• Step 1: Draw a circle with a radius of 1 unit.
• Step 2: Shift the radius by a certain angle.

Similar to degrees, radians can also be used in trigonometric calculations. To do this, you can adjust your calculator to display answers in radians by going to Options -> Angle Unit -> Radians. Let's put this into practice with an example.

Using Radians to Solve Trigonometry Equations

Let's say we want to find the value of angle CAB in radians. This is a standard trigonometry question that requires us to determine which method out of SOHCAHTOA we will be using. In this case, we have the opposite and adjacent sides, so we will apply the TOA method. Just remember to set your calculator to radians before the final step. Thus, angle CAB has a size of .

Let's explore another example to gain a better understanding of solving equations using radians.

Example: Finding the Value of

We can use the sine rule to solve this problem and don't forget to adjust your calculator to radians. This means that:

Now that we have learned how to convert our calculator to radians, what about converting between radians and degrees? Let's find out.

Converting Between Radians and Degrees

There is a simple conversion formula that we can use:

And vice versa:

Let's see this in action with an example.

Example: Converting to Radians

To convert to radians, simply multiply the degree value by and you will get .

Now, let's try it in reverse.

Example: Converting to Degrees

To convert to degrees, divide the radian value by and the result will be .

What We Have Learned

• Radians are an alternative angle unit used in solving trigonometry equations.
• A circle has 2π radians.
• To convert to radians, divide by 180 and multiply by π.
• The method for solving equations using radians is the same as with degrees.
• Remember to adjust your calculator to radians when solving problems.

In conclusion, radians are a valuable angle unit that can simplify equations in trigonometry. They offer a different approach and can prove to be a useful alternative to degrees. So, the next time you encounter a trigonometry problem, consider using radians as your angle unit to find a different perspective and possibly a simpler solution.