LESSON 4.1

Right Triangle Trigonometry

Lesson Overview:

a. Value of Special Angles and Tricks to Remember
b. SOH CAH TOA to Solve for Special Right Triangles
c. SOH CAH TOA to solve for Right Triangle sides
d. SOH CAH TOA to solve for Right Triangle Angles
e. Given the value of one Trig function solve for the rest

Part A: Value of Special Angles and Tricks to Remember

We define special angels in trigonometry as the following; 0, 30, 45, 60, and 90 degrees.
For each of these angles you must know the radian, the sine value, the cosine value, and the tangent value.

The following chart will help you with all this information:

To remember all this information, you can use the left-hand trick it goes as follows:

The new chart will look like this:

Part B: SOH CAH TOA to Solve for Special Right Triangles

Right triangles can be solved using the acronym SOH CAH TOA.

Sine= opp./hyp. Cosine= adj./hyp. Tangent= opp./adj.

Here are some examples on how to solve special right triangles:

Part C&D: SOH CAH TOA to solve for Right Triangle sides and Angles

You can also use SOH CAH TOA to solve for any right triangle sides or any angle measure within a right triangle by using your trig functions and givens.

How to Solve for Sides: How to Solve for Angles:

- All you must do is set the trig function you are using to the power of negative 1.

Part E: Given the value of one Trig function solve for the rest

This is the hardest topic of 4.1 to understand. Based on one given

trig function you must be able to obtain the other five.

To do this,we must first look at the following diagram.

SAT and ACT Testing on SOH CAH TOA

Youtube Video that shows

SOH CAH TOA at the SAT level:

Real World Examples of SOH CAH TOA

Now that you know the previous information, you can solve all trig functions in the first quadrant from one known

EXAMPLE:

There are two types of special right triangles;

One with two 45 degrees One with 30, 60, and 90

and one 90 degree angles: degrees:

There are major and minor functions in trigonometry. The major functions are sine, cosine, and tangent. The minor functions are inverses of these. The three minor functions are secant, cosecant, and cotangent.

The inverse of sine is cosecant; the inverse of cosine is secant, and the inverse of tangent is cotangent.

Based on this information we can fill out the previous chart with more information. Since the three minor functions are inverses of the major functions, all you need to do to solve for their values all you need to do is take the reciprocal.

Lesson Summary:

After lesson 4.1, you should be able to know all six trig functions for the special angles 0, 30, 45, 60, and 90 degrees. You should be able to use SOA CAH TOA to solve for special right triangles, or any right triangle sides and angles. Lastly, you should be able to find all other trig function in the first quadrant of the coordinate plane based on one given.

SUN

tan