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In National 4 Maths Trigonometry is used to find the size of a missing side or angle in a right-angled triangle using the sine, cosine or tangent ratios
- Right-Angled Triangle
- Sine, Cosine and Tangent
- Try Sin Cos and Tan
- Unit Circle
- Repeating Pattern
- Solving Triangles
- Other Functions
- Trigonometric and Triangle Identities
The triangle of most interest is the right-angled triangle. The right angle is shown by the little box in the corner: Another angle is often labeled θ, and the three sides are then called: 1. Adjacent: adjacent (next to) the angle θ 2. Opposite: opposite the angle θ 3. and the longest side is the Hypotenuse
The main functions in trigonometry are Sine, Cosine and Tangent They are simply one side of a right-angled triangle divided by another. For any angle "θ": (Sine, Cosine and Tangent are often abbreviated to sin, cos and tan.) The triangle could be larger, smaller or turned around, but that angle will always have that ratio. Calculators have sin, cos...
Play with this for a while (move the mouse around) and get familiar with values of sine, cosine and tangent for different angles, such as 0°, 30°, 45°, 60° and 90°. Also try 120°, 135°, 180°, 240°, 270° etc, and notice that positions can be positive or negative by the rules of Cartesian coordinates, so the sine, cosine and tangent change between po...
What you just played with is the Unit Circle. It is a circle with a radius of 1 with its center at 0. Because the radius is 1, we can directly measure sine, cosine and tangent. Here we see the sine function being made by the unit circle: Note: you can see the nice graphs made by sine, cosine and tangent.
Because the angle is rotating around and around the circle the Sine, Cosine and Tangent functions repeat once every full rotation (see Amplitude, Period, Phase Shift and Frequency). When we want to calculate the function for an angle larger than a full rotation of 360° (2π radians) we subtract as many full rotations as needed to bring it back below...
Trigonometry is also useful for general triangles, not just right-angled ones . It helps us in Solving Triangles. "Solving" means finding missing sides and angles. We can also find missing side lengths. The general rule is: When we know any 3 of the sides or angles we can find the other 3 (except for the three angles case) See Solving Trianglesfor ...
Similar to Sine, Cosine and Tangent, there are three other trigonometric functionswhich are made by dividing one side by another:
And as you get better at Trigonometry you can learn these: Enjoy becoming a triangle (and circle) expert!
Trigonometry (from Ancient Greek τρίγωνον (trígōnon) 'triangle' and μέτρον (métron) 'measure') [ 1 ] is a branch of mathematics concerned with relationships between angles and side lengths of triangles. In particular, the trigonometric functions relate the angles of a right triangle with ratios of its side lengths.
Sine, Cosine and Tangent (often shortened to sin, cos and tan) are each a ratio of sides of a right angled triangle: For a given angle θ each ratio stays the same. no matter how big or small the triangle is. To calculate them: Divide the length of one side by another side. Example: What is the sine of 35°?
Trigonometry, the branch of mathematics concerned with specific functions of angles. There are six functions commonly used in trigonometry: sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc). Learn more about trigonometry in this article.
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) [1] are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
Mar 26, 2016 · The six trig functions are named sine, cosine, tangent, cotangent, secant, and cosecant. Many people confuse the spoken word sine with sign — you can't really tell the difference when you hear it unless you're careful with the context.
