Trigonometry

Trigonometry can be used to help us find the Angles and distances of triangles. In GCSE Mathematics, you will have come across **sine, cosine ** and **tangent ** - Functions that come from the Angles and distances of a right-angled triangle. Three other Functions are the reciprocals of these familiar Functions. They are **secant** (sec), **cosecant** (cosec) and **cotangent** (cot) respectively.

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Jetzt kostenlos anmeldenTrigonometry can be used to help us find the Angles and distances of triangles. In GCSE Mathematics, you will have come across **sine, cosine ** and **tangent ** - Functions that come from the Angles and distances of a right-angled triangle. Three other Functions are the reciprocals of these familiar Functions. They are **secant** (sec), **cosecant** (cosec) and **cotangent** (cot) respectively.

You can use Trigonometric Functions to help you find the angles and lengths of sides in triangles. The first step is to label your triangle with opposite, adjacent and hypotenuse; the diagram below shows you how to label your triangle correctly.

SOHCAHTOA is an acronym to help you remember which function you need to use when using trigonometry to find an angle or the length of a side in a triangle. They are broken down for you below:

These Equations help you to find the missing length of a side in a right-angled triangle. Here are the steps:

Label your triangle with hypotenuse, opposite, adjacent, as shown in the diagram above.

Choose the equation that you need to use based on the information you have from the triangle.

Substitute your figures into the equation

Use your calculator and the sin, cos, tan buttons to find your missing length.

If you need to find the missing angle in your triangle, you can still use SOHCAHTOA but with the **inverse ** of the sin, cos and tan functions. Here are the Equations for finding the missing angle:

Find the value of x

To do this, we label our triangle, with hypotenuse, opposite and adjacent, shown below.

You can see that you have got the value of the opposite side, and you are looking for your hypotenuse.

Using SOHCAHTOA, your calculation involves the O and the H. The part of SOHCAHTOA that includes both of these letters is SOH. Therefore you need to use **sine** to find the value of x;

$\mathrm{sin}\theta =\frac{opposite}{hypotenuse}$

Now you can substitute your values into the formula and rearrange it to solve for x;

$\mathrm{sin}55=\frac{16}{x}$

$x=\frac{16}{\mathrm{sin}55}$

$x=19.5$

Trigonometry can be used to find the angles and side lengths for non-right-angled triangles too. To do this, you use the **sine** and **cosine ** rules.

When using these rules, you first need to label the triangle to help you see which function to use.

When labeling the triangle, it doesn't matter which angles are which, as long as the sides are correctly matched to their opposite angle.

You can use the cosine rule to find the length of a missing side when you know the other two sides and the angle between them. The formula to use is:

You can also use the cosine rule to find an angle if you know all of the lengths of the sides. Here, the formula is:

You can use the sine rule to find the length of a side or the angle of a triangle. The formula used to find the side length is below:

The formula for a missing angle is:

Let's have a look at an example and decide which rule would be best to use.

Find the value x

Looking at this example, you can see that the missing quantity x is at an angle. You have also been given the side lengths for all three sides, and because of this, you can use the cosine rule - specifically, the formula used to find an angle.

If you know the lengths of two sides of any triangle and the angle between them, you can find the area of the triangle. The formula for this is:

Let's look at this triangle and think about how we put the information into our formula.

First, you need to label your triangle, and then you can substitute the information into the formula;

$area=\frac{1}{2}abS\mathrm{in}C$

$area=\frac{1}{2}\left(15\right)\left(12\right)Sin70$$area=85.6c{m}^{2}$

A Unit Circle can help you understand the Trigonometric Functions, the circle has a radius of 1, and the center coordinates are (0,0). This means that when you calculate the trigonometric values, you will get a coordinate point on the circle, known as (x, y).

To find the gradient of p, you use

Trigonometry is used to help us find the lengths and angles of triangles.

The trigonometric functions are sine, cosine, tangent, sec, cosec and cot.

The acronym SOHCAHTOA helps you to remember the correct function to use.

The Sine and Cosine Rules can be used when finding angles or side lengths of non-right-angled triangles.

A Unit Circle helps you to understand trigonometric functions.

Trigonometry is a mathematical topic which looks at the relationship between angles and distances.

**trigon**, which means triangle and **metron**, which means to measure.

What are the three trigonometric functions?

Sine, cosine and tangent

What are the names of the three sides of a right-angled triangle?

Hypotenuse, opposite and adjacent

How do you find the length of a side in a non-right-angled triangle?

You can use the sine or cosine rule.

When would you use the sine rule?

You would use the sine rule when finding the missing side length or angle when you have two opposite sides and angles.

What is the equation for tan?

opposite/ adjacent

What is the equation for secant?

Hypotenuse divided by adjacent.

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