Content:
MA5-TRG-P-01
Solve 3-dimensional problems involving right-angled triangles
- Apply Pythagoras’ theorem to solve problems involving the lengths of the edges and diagonals of rectangular prisms and other 3-dimensional objects
- Apply trigonometry to solve problems involving right-angled triangles in 3 dimensions, including using bearings and angles of elevation and depression
Apply the sine, cosine and area rules to any triangle and solve related problems
- Use graphing applications to verify the sine rule asinA=bsinB=csinC and that the ratios of a side to the sine of the opposite angle is a constant
- Apply the sine rule in a given triangle ABC to find the value of an unknown side
- Apply the sine rule in a given triangle ABC to find the value of an unknown angle (ambiguous case excluded): sinAa=sinBb=sinCc
- Use graphing applications to verify the cosine rule c2=a2+b2−2abcosC
- Apply the cosine rule to find the unknown sides for a given triangle ABC
- Rearrange the formula to deduce that cosC=a2+b2−c22ab and use this to find an unknown angle
- Use graphing applications to verify the area rule A=12absinC
- Apply the formula A=12absinC, where a and b are the sides that form angle C to find the area of a given triangle ABC
- Solve problems involving finding unknown angles or sides in triangles (excluding right-angled triangles) by selecting and applying the appropriate rule
MA5-TRG-P-02
Use the unit circle to define trigonometric functions and represent them graphically
- Redefine the sine and cosine ratios in terms of the unit circle
- Verify that the tangent ratio can be expressed as a ratio of the sine and cosine ratios
- Use graphing applications to examine the sine, cosine and tangent ratios for (at least) 0∘≤x≤360∘, and graph the results
- Use graphing applications to examine graphs of the sine, cosine and tangent functions for angles of any magnitude, including negative angles
- Use the unit circle or graphs of trigonometric functions to establish and apply the relationships sinA=sin(180∘−A), cosA=−cos(180∘−A), and tanA=−tan(180∘−A) for obtuse angles when 0∘≤A≤90∘
- Establish and apply the relationship m=tanθ where m is the gradient of the line and θ is the angle of inclination of a line with the x-axis on the Cartesian plane
Solve trigonometric equations using exact values and the relationships between supplementary and complementary angles
- Derive and apply the exact sine, cosine and tangent ratios for angles of 30∘, 45∘ and 60∘
- Verify and use the relationships between the sine and cosine ratios of complementary angles in right-angled triangles: sinA=cos(90∘−A) and cosA=sin(90∘−A)
- Find the possible acute and/or obtuse angles, given a trigonometric ratio
- Apply the sine rule and area rule to find angles involving the ambiguous case