Tuesday 5 January 2016

IGCSE Trigonometry

January 05, 2016 Year 10, Year 11 No comments

Topics For 2016 Trigonometri Exam

1. Bearing
2. Phytagoras Theorem
3. Trigonometric Ratio
4. Angle of elevation and depression
5. Sine and cosine value
6. Sine and Cosine Rule
7. Area of triangle
8. Angle between Line and Plane

1. Bearing

2. Pythagoras Theorem

3. Trigonometric Ratio

4. Angle of elevation and depression

5. Sine and cosine value

6. Sine and Cosine Rule

7. Area of triangle

8. Angle between Line and Plane

Monday 4 January 2016

A Level Trigonometry

January 04, 2016 Year 10, Year 11 No comments

1. Sketching and Using graph of Trigonometric Function

Graphs of Sine, Cosine and Tangent

Here are some nice graphs to look at ...

Plot of Sine

The Sine Function has this beautiful up-down curve (which repeats every 2π radians, or 360°).

It starts at 0, heads up to 1 by π/2 radians (90°) and then heads down to -1.

Plot of Cosine

Cosine is just like Sine, but it starts at 1 and heads down until π radians (180°) and then heads up again.

Plot of Sine and Cosine

In fact Sine and Cosine are like good friends: they follow each other, exactly "π/2" radians, or 90°, apart.

Plot of the Tangent Function

The Tangent function has a completely different shape ... it goes between negative and positive Infinity, crossing through 0 (every π radians, or 180°), as shown on this plot.

At π/2 radians, or 90° (and -π/2, 3π/2, etc) the function is officially undefined, because it could be positive Infinity or negative Infinity.

Equation Grapher

Description :: All Functions

Enter an Equation using the variables x and/or y and an =, press Go:

Completed in 0,096s

Zoom:

(Note: there is also the Flash Version.)

Description

It can plot an equation where x and y are related somehow (not just y=...), like these:

Examples:

x^2+y^2=9 (an equation of a circle with a radius of 3)
sin(x)+cos(y)=0,5
2x-3y=1
cos(x^2)=y
(x-3)(x+3)=y^2
y=x^2

If you don't include an equals sign, it will assume you mean "=0"

It has not been well tested, so have fun with it, but don't trust it.

If it gives you problems, let me know.

Note: it may take a few seconds to finish, because it has to do lots of calculations.

If you just want to graph a function in "y=..." style you may prefer Function Grapher and Calculator

Zooming

Use the zoom slider (to the left zooms in, to the rigth zooms out).

To reset the zoom to the original bounds click on the Reset button.

Dragging

Click-and-drag to move the graph around. If you just click-and-release (without dragging), then the spot you clicked on will be the new center

Note: the plots use computer calculations. Round-off can cause errors or values can be missed completely.

All Functions

Operators

	+	Addition operator
	-	Subtraction operator
	*	Multiplication operator
	/	Division operator
	^	Exponent (Power) operator

Functions

	sqrt	Square Root of a value or expression.
	sin	sine of a value or expression
	cos	cosine of a value or expression
	tan	tangent of a value or expression
	asin	inverse sine (arcsine) of a value or expression
	acos	inverse cosine (arccos) of a value or expression
	atan	inverse tangent (arctangent) of a value or expression
	sinh	Hyperbolic sine (sinh) of a value or expression
	cosh	Hyperbolic cosine (cosh) of a value or expression
	tanh	Hyperbolic tangent (tanh) of a value or expression
	exp	e (the Euler Constant) raised to the power of a value or expression
	ln	The natural logarithm of a value or expression
	log	The base-10 logarithm of a value or expression
	floor	Returns the largest (closest to positive infinity) value that is not greater than the argument and is equal to a mathematical integer.
	ceil	Returns the smallest (closest to negative infinity) value that is not less than the argument and is equal to a mathematical integer.
	round	Round to the nearest integer. Examples: round(-2,5) = -2, round(-0,1) = 0, round(0,1) = 0, round(2,5) = 3
	abs	Absolute value (distance from zero) of a value or expression
	sign	Sign (+1 or -1) of a value or expression