Pre-Calculus
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Table of Contents
1. Converting Degrees to Radians and Back
2. Unit Circle
3. Periodic Functions
4. Coterminal Angles
5. Initial and Terminal Side
Trig Functions
6. Graph of Sine Function
7. Graph of Cosine Function
8. Graph of Tangent Function
9. Graph of Secant Function
10. Graph of Cosecant Function
11. Graph of Cotangent Function
12. Graph of All Inverse Trig Functions
13. Real World Applications of Sinusoids
Trig Identities
14. Sum and Difference Identities
15. Pythagorean Identities
16. Double Angle Identities
17. Power Reducing Identities
18. Half-Angle Identities
19. Law of Sines
20. Law of Cosines
21. Mathematical Induction
22. Graphing Polar Curves, Roses
23. How to use an R, Theta Table to Graph
24. Basic Statistics
Sources
law of cosines
The Law of Cosine has three forms:
a
²=b
²+c
²
-2bc cos(A)
b
²=
a²+c
²
-2ac cos(B)
c
²=a
²+b
²
-2ab cos(C)
Before solving the problem, you have to decide which formula to use. It depends on which side length or angle you are solving for.
Extra Information:
The law of cosines looks similar to the Pythagorean Theorem.
And lower case letters in the law of cosines represent the side lengths of a triangle, while the capitalized letters represent angles.
The Law of Cosine is only used when:
Two sides and the angle between them (SAS) is known and we are trying to solve for the third side
All three sides is given (SAS) and all the angles of the triangle can be solved
To use the formula, substitute accordingly (side a for a and so forth).
The concept is straightforward, so don't over think it!
Start with: c
²
= a
²
+ b
²
− 2ab cos(C)
Put in a, b and c: 8
²
= 9
²
+ 5
²
− 2 × 9 × 5 × cos(C)
Calculate: 64 = 81 + 25 − 90 × cos(C)
Subtract 25 from both sides: 39 = 81 − 90 × cos(C)
Subtract 81 from both sides: −42 = −90 × cos(C)
Swap sides: −90 × cos(C) = −42
Divide both sides by −90: cos(C) = 42/90
Inverse cosine: C = cos-1(42/90)
Calculator: C =
62.2°
(to 1 decimal place)