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UbD 6 Page Template
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Unit Cover Page
Unit title Trigonometry in a right angled triangle and in any scalene triangle
Grade Year 10
Subject/Topic Areas IGCSE Trigonometry
Key words hypotenuse, opposite, adjacent, square, square root, tangent, sine, cosine, inverse
function, 3 figure bearing, angle of elevation, angle of depression, plane, line
projection
Designed by
Janet Chambers
Time Frame 3 weeks
School district
Dhahran
School
Dhahran British Grammar School
Brief summary of unit (including curricular and unit goals)
This unit introduces the concepts of basic trigonometric ratios (sine, cosine, tangent), their
relationship to the sides and angles in a right angled triangle and their application to finding missing
sides and angles. The sine and cosine rules will be applied in non right angled triangles to find
missing sides and angles. The area of a triangle is calculated by extending the ½bh formula to any
triangle. All will be applied to simple trigonometric problems in [2D] and [3D], and to real world
applications in navigation and surveying. The properties of the sine and cosine curve will be used to
solve simple trigometric equations.
IGCSE curriculum objectives
 Apply Pythagoras’ theorem and the sine, cosine and tangent ratios for acute angles to the
calculation of a side or of an angle of a right-angled triangle
 Use simple examples involving the sine, cosine and tangent ratios to calculate the length of
an unknown side of a right-angled triangle given an angle and the length of one side.
 Use simple examples involving inverse ratios to calculate an unknown angle given the
length of two sides of a right-angled triangle.
 Re-state Pythagoras’ theorem.
 Interpret and use three-figure bearings measured clockwise from the north. Discuss how
bearings are measured and written.
 Solve trigonometrical problems in two dimensions involving angles of elevation and
depression,
 Extend sine and cosine functions to angles between 90o and 180 o ,
 Solve problems using the sine and cosine rules for any triangle and the formula area of
triangle = ½absinC;
 Solve simple trigonometrical problems in three dimensions including angle between a line
and a plane.
 Draw a sine and cosine curve and discuss its properties.
 Define angles of elevation and depression.
 Use straightforward examples to illustrate how to solve problems using the sine and cosine
rules.
Janet Chambers
Page 1
6/25/2017
UbD 6 Page Template
Page 2
Stage 1 – Identify Desired Results
Established goals
G
Students will recognize and use spatial relationships in two and three dimensions to solve problems.
Students will recall, apply and interpret mathematical knowledge in the context of navigation and
surveying situations.
Students will understand and use the trigonometric ratios for sine cosine and tangent
Students will understand and use the area formulae for triangles
Students will understand and use the formula for the sine and cosine rules
Students will understand and use the repetitive and reflective nature of the sine and cosine curves to
solve trigonometric equations 0 < x < 360
What understandings are desired?
U
Students will understand that….
Geometric relationships and measurements help us solve problems and make sense of our world.
Trigonometric functions are used to model real world problems.
What essential questions will be considered?
Q
Why is the trigonometric value of any angle the same regardless of the size of the triangle?
How can knowledge of triangles and trigonometric ratios help you find missing sides or angles?
What use is trigonometry in navigation, surveying and triangulation?
What is the importance of the sine curve?
What key knowledge and skills will students acquire as a result of this unit?
Students will know ….
 the formula for sine cosine and tangent ratios applied to right angled triangles
 the sine and cosine rules
 the formula for the area of any triangle
 how to represent bearings and angles of elevation/depression in diagrams.
K
Students will be able to ……
S
 recognize hypotenuse, opposite and adjacent sides given the angle in a right angled triangle
 find missing sides or angles in a right angled triangle using Pythagoras theorem or
trigonometric ratios
 recognize when to apply the sine or cosine rule and use it to find missing sides or angles
given SSS, SSA, or SAS.
 use a scientific calculator to evaluate trigonometric functions and their inverses
 create diagrams to represent the movement of ships/planes and use them to solve navigation
problems
 apply trigonometric functions in [2D] and [3D] problems to find sides and angles
 find the area of triangles using ½ absinC
 draw the sine and cosine curves and use them to solve trigonometric equations, 0 < x < 360
Janet Chambers
Page 2
6/25/2017