Angles play a large role in Trigonometry. It is important to know whether the angle is measured in radians or degrees. It is also to know the difference between positive and negative angles. Videos in this section will address different types of angles and their measurements.Â
Measurements of Angles
Positive vs Negative Angles
Types of Angles
Find Measures of Complementary
or Supplementary Angles
Find Complement and Supplement of Angle (in Radians)
Converting Degrees to Degrees, Minutes, and Seconds (DMS)
Converting Degrees, Minutes, and Seconds (DMS)to Degrees
Converting DMS to Degrees, and Vice Versa in the TI-84
Converting DMS to Degrees, and Vice Versa in the TI-Nspire
Adding and Subtracting with Degrees, Minutes, Seconds
Adding and Subtracting with Degrees, Minutes, Seconds TI-84
Adding and Subtracting with Degrees, Minutes, Seconds TI-Nspire
Standard Position of Angles in
the Coordinate Plane
Coterminal Angles
Find Measure of Coterminal Angle
of Least Positive Degree
Sketch an Angle in Standard Position and Find the Closest Positive and Negative Coterminal Angle
Finding arc length is an important part of Trigonometry. Learn how to find the length of the arc using the formula, as well as applications of finding arc length.
Arc Length
Find Central Angle Given Arc Length and Radius
Find Radius Given Arc Length and Central Angle
Find North-South Distance
Given Latitude
Right Triangle Trig
Being able to solve a right triangle is one of the most important aspects of Trigonometry. Knowing when to use sine, cosine, and tangent are key components in Trigonometry. I find the easiest way to remember how to use the trig functions is to memorize SOH-CAH-TOA. Sine is always the Opposite divided by the Hypotenuse. Cosine is always the Adjacent divided by the Hypotenuse. Tangent is always Opposite divided by Adjacent. It is important to label the triangle with the parts when first beginning to help you know which function to use. The hypotenuse is always across from the right angle and is the longest side. The adjacent is the side touching the angle you are working with that is not the hypotenuse. The opposite side is the side not touching the angle.
Solve a Right Triangle
Applications
Angle measures and arc lengths have several applications in a trigonometry course. Different applications include finding area of sectors, finding linear speed of a point on a circle, and finding angular rotation.
Area of a Sector
Linear and Angular Speed Formulas
Using Linear and Angular Speed Formulas
Find Angular Speed of a Pulley and Linear Speed of a Belt
Find Distance Bicycle Moves when Pedals are Turned
The Unit Circle
The unit circle plays a large role in Trigonometry. Learn how to set up the unit circle, and important aspects of the unit circle.
Unit Circle: Degree and Radian Measures
Special Right Triangles Used in Setting up the Coordinates of the Unit Circle
Coordinates of the Unit Circle
Circular (Trigonometric) Functions in the Unit Circle
Find the Six Trigonometric Functions Using the Unit Circle
Use the Unit Circle to Find Exact Trig Values
Find Trig Functions
Being able to find the six trigonometric functions is very important. Understanding how to find sine, cosine, tangent, cotangent, cosecant, and secant in right triangles is very important. There are many ways that the problems can be presented. For example, you might be given a point on a circle and be asked to find the trig functions. Depending on the level you are at, sometimes you will only be asked to find sine, cosine, and tangent.
Find 6 Trig Functions Given a Point on the Circle
Find Remaining Trig Functions Given Sine and Quadrant II
Find Remaining Trig Functions Given Tangent and Quadrant III
Evaluate Trig Functions
Being able to evaluate trig functions is very important in Trigonometry. Trig tables were used before scientific calculators were so readily available. Learn how to use a calculator to find the given function.
Evaluate Trig Functions Using the TI-Nspire
Evaluate Trig Functions Using the TI-84
Evaluate Trig Functions Using Desmos
Evaluate Trig Functions Given Degrees, Minutes, and Seconds Using the TI-84
Evaluate Trig Functions Given Degrees, Minutes, and Seconds Using the TI-Nspire