TABLE OF CONTENTS
1. -trigonometry
- angles-and-triangles
- trigonometric-ratios
- identities-and-equations
- graphs-and-functions
2. -calculus
- limits
- differentiation
- integration
- applications
TRIGONOMETRY:
Angles and Triangles-*. Angles*: Measured in degrees or radians
Triangles*: Right-angled, obtuse, acute
Pythagorean Theorem*: $a^2 + b^2 = c^2$.
Example:
:* Find the length of the hypotenuse of a right-angled triangle with legs 3 and 4.
- $c^2 = 3^2 + 4^2 = 9 + 16 = 25$
- $c = \sqrt{25} = 5$
Trigonometric Ratios
- *Sine*: $\sin(\theta) = \frac{opposite}{hypotenuse}$
- *Cosine*: $\cos(\theta) = \frac{adjacent}{hypotenuse}$
- *Tangent*: $\tan(\theta) = \frac{opposite}{adjacent}$
*Example:* Find $\sin(30^\circ)$.
- $\sin(30^\circ) = \frac{1}{2}$
Identities and Equations
- Pythagorean Identity*: $\sin^2(\theta) + \cos^2(\theta) = 1$
-PythagoreanTheorem: $\sin(A+B) = \sin(A)\cos(B) + \cos(A)\sin(B)$
*Example:* Simplify $\sin^2(x) + \cos^2(x)$.
- $\sin^2(x) + \cos^2(x) = 1$
Graphs and Functions
- *Sine and Cosine Graphs*: Periodic, amplitude 1
1. -trigonometry
- angles-and-triangles
- trigonometric-ratios
- identities-and-equations
- graphs-and-functions
2. -calculus
- limits
- differentiation
- integration
- applications
TRIGONOMETRY:
Angles and Triangles-*. Angles*: Measured in degrees or radians
Triangles*: Right-angled, obtuse, acute
Pythagorean Theorem*: $a^2 + b^2 = c^2$.
Example:
:* Find the length of the hypotenuse of a right-angled triangle with legs 3 and 4.
- $c^2 = 3^2 + 4^2 = 9 + 16 = 25$
- $c = \sqrt{25} = 5$
Trigonometric Ratios
- *Sine*: $\sin(\theta) = \frac{opposite}{hypotenuse}$
- *Cosine*: $\cos(\theta) = \frac{adjacent}{hypotenuse}$
- *Tangent*: $\tan(\theta) = \frac{opposite}{adjacent}$
*Example:* Find $\sin(30^\circ)$.
- $\sin(30^\circ) = \frac{1}{2}$
Identities and Equations
- Pythagorean Identity*: $\sin^2(\theta) + \cos^2(\theta) = 1$
-PythagoreanTheorem: $\sin(A+B) = \sin(A)\cos(B) + \cos(A)\sin(B)$
*Example:* Simplify $\sin^2(x) + \cos^2(x)$.
- $\sin^2(x) + \cos^2(x) = 1$
Graphs and Functions
- *Sine and Cosine Graphs*: Periodic, amplitude 1
