Second Semester Geometry
Survival Guide
Chapter 8: Trigonometry
Key Ideas
- Pythagorean Theorum
- SOH-CAH-TOA Trigonomic Device
- Inverse ""
- Degree and Radian Measures
- Special Right Triangles
- Unit Circle
Pythagorean Theorum
A squared + B squared = C squared (base squared + height squared = hypothenuse [longest side])
- Only works on right triangles
Trigonometric Ratios
- The sides and the angles of triangles and the trigonometric functions are related.
- SOH CAH TOA
- Shows what the missing side measure is
What SOH CAH TOA stands for
The opposite/adjacent/hypotenuse refers to what side it is in comparison to the angle measurement given.
Where the Sides Are
Angle A is the given angle measurement in this case.
Example Problem
The missing side was cut off at the bottom.
Inverse Trigonometric Functions
- Shows what the missing side measure is
- Sets it up like the picture shown
Angle of Elevation/Depression
- Deals with viewpoint of people/things
- Used to find out how high or at what angle things are at
Angle of Elevation
Calculate by using SOH CAH TOA
Angle of Depression
congruent to the angle of elevation
BOTH COMBINED IN THE SAME PICTURE
MIND BLOWN
6 Trig Functions
Pretty straight forward. The formulas are in the picture. They are sine, cosine, tangent, cosecant, secant, and cotangent.
Degree and Radian Measures
You can measure with both degrees and radians. In a unit circle, there are degrees and radians. The degree is obviously the angle measure of each angle, and the radian measure is what it is in terms of Pi.
- To rewrite a degree measure in radians, multiply be Pi radians over 180 degrees, and the reciprocal of that for radians to degree measure.
- You use the unit circle in these problems.
Special Right Triangles
Theorem: In a 30-60-90 triangle the sides are in the ratio 1:2:the square root of 3
Tips!
- Use a calculator it makes your life much easier
- Don't overthink the problem
- Write out ALL your work
Things We Struggled With
- The Unit Circle and Radians. That was just hard to understand.
- Angle of Depression was hard at first, but with practice it got easier.