2.3: Six Trigonometric Functions and Radians
While working in your math class one day, you are given a sheet of values in radians and asked to find the various trigonometric functions of them, such as sine, cosine, and tangent. The first question asks you to find the
Do you think this is possible? As it turns out, it is indeed possible to apply trig functions to measurements in radians. Here you'll learn to do just that.
At the end of this Concept, you'll be able to compute
Watch This
James Sousa: Determine Exact Trig Function Values With the Angle in Radians Using the Unit Circle
Guidance
Even though you are used to performing the trig functions on degrees, they still will work on radians. The only difference is the way the problem looks. If you see
Most scientific and graphing calculators have a MODE setting that will allow you to either convert between the two, or to find approximations for trig functions using either measure. It is important that if you are using your calculator to estimate a trig function that you know which mode you are using. Look at the following screen:
If you entered this expecting to find the sine of 30 degrees you would realize that something is wrong because the answer should be
Scientific calculators will usually have a 3letter display that shows either DEG or RAD to tell you which mode the calculator is in.
Example A
Find
Solution: If needed, convert
Example B
Find the value of
Solution: If needed, convert
Example C
Convert 1 radian to degree measure.
Solution: Many students get so used to using
So 1 radian would be
Vocabulary
Radian: A radian (abbreviated rad) is the angle created by bending the radius length around the arc of a circle.
Guided Practice
1. Using a calculator, find the approximate degree measure (to the nearest tenth) of the angle expressed in radians:
2. Using a calculator, find the approximate degree measure (to the nearest tenth) of the angle expressed in radians:
3. Gina wanted to calculate the
Fortunately, Kylie saw her answer and told her that it was obviously incorrect.
 Write the correct answer, in simplest radical form.
 Explain what she did wrong.
Solutions:
1.
2.
3. The correct answer is
Concept Problem Solution
As you have learned in this Concept, the
Practice
Using a calculator, find the approximate degree measure (to the nearest tenth) of the angle expressed in radians.

4π7 
5π6 
8π11 
5π3 
8π3 
7π4 
12π5
Find the value of each using your calculator.

sin3π2 
cosπ2 
tanπ6 
sin5π6 
tan4π3 
cot7π3 
sec11π6  Do you think radians will always be written in terms of
π ? Is it possible to have, for example, exactly 2 radians?