TRIGONOMETRY

Learning ObjectiveStudents will be able to APPLY the concept of TRIGONOMETRY in real - life problems

Student's Activity of mathematics that deals with the relationship between the side lengths and angle of triangles. We

1. Brief Explanation of Trigonometry Concepts

TRIGONOMETRY is a branch of mathematics that deals with the relationship between the side lengths and angles of triangles

We can use trigonometric ratios to find unknown side lengths and angles in right angled triangles.

FINDING SIDE LENGTHS

Suppose we are given the angles of a right angled triangle, and the length of a side. We can use the trigonometric ratios to find the other side lengths.

Step 1 : Redraw the figure and mark on it HYP, OPP, and ADJ relative to a given angle.

Step 2 : Choose an appropriate trigonometric ratio, and construct an equation.

Step 3 : Solve the equation to find the unknown side length

FINDING ANGLES

If we know two side lengths of a right angled triangle, we can use trigonometry to find the angles. If In the right angled triangle shown sin A = 3/5, we say that A is the INVERSE SINE of 3/5. We can use a calculator to evaluate inverse sines.

PROBLEM SOLVING USING TRIGONOMETRY

The trigonometric ratios can be used to solve a wide variety of problems involving right angled triangles. When solving these problems it is important to follow the steps below:

* Draw a DIAGRAM to illustrate the situation

* Mark on the diagram the UNKNOWN angle or side that needs to be calculated

* Locate a RIGHT ANGLED TRIANGLE in your diagram

* Write an EQUATION connecting an angle and two sides of the triangle using an appropriate trigonometric ratio

* SOLVE the equation to find the unknown

* WRITE your answer in sentence form

ANGLES OF ELEVATION AND DEPRESSION

When an object is HIGHER than an observer, the ANGLE OF ELEVATION is the angle from the horizontal UP to the object.

When an object is LOWER than an observer, the ANGLE OF DEPRESSION is the angle from the horizontal DOWN to the object.

THE AREA OF A TRIANGLE

We can use trigonometry to find the area of a triangle if we are given the lengths of TWO SIDES, as well as the INCLUDED ANGLE between the sides.

The area of a triangle is a half of the product of two sides and the sine of the included angle.

Area = 1/2 x ab sin C

THE SINE RULE

The sine rule is a set of equations which connects the lengths of the sides of any triangle with the sines of the opposite angles.

sin A/a = sin B/b = sin C/c

If we are given two angles and one side of a triangle, we can use the sine rule to find another side length. Finding angles using the sine rule is more complicated than finding sides because there may be two possible answers.

THE COSINE RULE

The cosine rule relates the three sides of a triangle and one of its angles. If we are given two sides of a triangle and the included angle, we can use the cosine rule to find the third side.

PROBLEM SOLVING USING THE SINE AND COSINE RULES

When using trigonometry to solve problems, you should draw a diagram of the situation. The diagram should be reasonably accurate, and all important information should be clearly marked on it

2. Making a Clinometer (please read or search from the internet how to make it)

Material Needed

1. Protractor

2. Straw

3. Sellotape

4. String

5. Glue Tac

* Take data for measuring height of object (Outdoor and Indoor ) Min 1 Object and Max 3 Object with 3 different data

Wednesday, 10th May 2017 : Outdoor Objects

Thursday, 18th May 2017 10.45 - 11.30 : Indoor Objects (Min 1 objects and Max 3 objects) Every objects should take 3 times

* Make a written report (Every Thursday, 18th & 25th May 2017 --> 1 Period)

- Title (Created by students)

- Introduction (Explain about concepts use in this investigation such as Pythagora's Theorem , basic trigonometry)

- Purpose of Investigation

- Procedure (include pictures)

1. Making Clinometer

2. Measuring Objects (Indoor and Outdoor)

- Table Data

1. Indoor Objects

2. Outdoor Objects

- Calculation

- Analysing and Conclusion

- Resources

Deadline : Wednesday, 31st May 2017

3. Practice to apply the concepts of basic trigonometry from their textbook

Exercise 12.A1 No. 1bf, 2behk, 3c, 4 --> Monday, 15th May 2017

Exercise 12.A2 No. 1efhi, 2c, 3 --> Monday, 15th May 2017

Exercise 12B No. 1 - 16 --> Wednesday, 17th May 2017

Exercise 12F No. 1bc, 3ac, 4ab, 5 - 8 --> Monday, 22nd May 2017

Exercise 12G1 No. 1ab, 2bc, 3, 4bc --> Wednesday, 24th May 2017

Exercise 12G2 No. 2, 3cd, 4c --> Wednesday, 24th May 2017

Exercise 12I No. 1 - 4, 10 - 11 --> Monday, 29th May 2017

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