Welcome!!!
This is a student-generated webpage that explores the basics of Trigonometry. The purpose of this webpage is to touch on the many aspects of Trigonometry and to review previously learned concepts for the Honors Precalculus final. Here you will find original explanations and examples of topics such as the Unit Circle and Trig Identities.
Radian Measure: Radian = measure of central angle of circle (as long as arc length is equivalent to radius length!)
Radian Measure: Radian = measure of central angle of circle (as long as arc length is equivalent to radius length!)
Conversion Between Radian and Degree Measure:
Use the following diagram!
Use the following diagram!
EXAMPLE: Convert 60 degrees to radians.
From looking at the above equations, we know we must multiply by pi/180.
60 x pi/180 = pi/3 radians
Convert 5pi/6 radians to degrees.
Now we know we must multiply by 180/pi.
5pi/6 x 180/pi = 150 degrees
From looking at the above equations, we know we must multiply by pi/180.
60 x pi/180 = pi/3 radians
Convert 5pi/6 radians to degrees.
Now we know we must multiply by 180/pi.
5pi/6 x 180/pi = 150 degrees
Standard Position: For an angle to be in standard position, the origin must be its vertex, and it must have one ray on the positive x axis.
Positive and Negative Angle Measures:
We all know that pi/6 is a positive angle and its graph lies in the first quadrant and we graph it counterclockwise, beginning at the positive x-axis.
What if a negative sign is placed in front of that angle measure?
What does that mean?
Instead of moving counterclockwise from the positive x-axis, we move clockwise to find the negative angle measure. So, -pi/6 is equal to the positive angle of 11pi/6.
We all know that pi/6 is a positive angle and its graph lies in the first quadrant and we graph it counterclockwise, beginning at the positive x-axis.
What if a negative sign is placed in front of that angle measure?
What does that mean?
Instead of moving counterclockwise from the positive x-axis, we move clockwise to find the negative angle measure. So, -pi/6 is equal to the positive angle of 11pi/6.
Coterminal Angles:
Coterminal angles share an initial side on the positive x-axis and a terminal side that can fall anywhere on the graph. They have different angle measures.
EXAMPLE:
The starting angle is 60°. What are its coterminal angles?
One angle can be found by reaching the terminal side in the clockwise (negtive) direction. The angle would be
-300°. (360-60=300)
The second angle can be found by going all the way around the unit circle counterclockwise and back to the terminal side. This angle would be 420°. (360+60=420)
Refer to the following graph for an additional help:
Coterminal angles share an initial side on the positive x-axis and a terminal side that can fall anywhere on the graph. They have different angle measures.
EXAMPLE:
The starting angle is 60°. What are its coterminal angles?
One angle can be found by reaching the terminal side in the clockwise (negtive) direction. The angle would be
-300°. (360-60=300)
The second angle can be found by going all the way around the unit circle counterclockwise and back to the terminal side. This angle would be 420°. (360+60=420)
Refer to the following graph for an additional help:
Quadrantal Angles:
Quadrantal angles are coterminal angles with their terminal side on the axes.
For example, if an angle's terminal side lies on the negative x-axis, it would be a quadrantal angle with angle measure 180°.
Quadrantal angles are coterminal angles with their terminal side on the axes.
For example, if an angle's terminal side lies on the negative x-axis, it would be a quadrantal angle with angle measure 180°.
Reference Angles:
Aside from quadrantal angles, all angles in standard position have their own reference angles.
Reference angles are always acute ;)
Aside from quadrantal angles, all angles in standard position have their own reference angles.
Reference angles are always acute ;)
They are angles between the terminal side of the angle you are working with and the x-axis.
These were some quick but important trig lessons. Explore the rest of the website to learn more!!!