Trigonometry D

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Trigonometry D (Path) | NSW Curriculum Website

• MA5-TRG-P-02 establishes and applies the properties of trigonometric functions and finds solutions to trigonometric equations

📖 Prior Knowledge

Content	Prerequisite relationships
Trigonometry A	- Define the trigonometric ratios → Define sine and cosine using the unit circle - Define the trigonometric ratios → Derive exact trigonometric ratios - Define the trigonometric ratios → Use complementary-angle relationships
Linear Relationships C	- Apply the gradient formula → Relate gradient to angle of inclination
Trigonometry C	- Apply the sine rule to find an angle → Apply the ambiguous case of the sine rule

Use the unit circle to define trigonometric functions and represent them graphically.pdf

• 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) $0°\le \theta \le 360°$, 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 $\sin A=\sin \left(180°-A\right)$, $\cos A=-\cos \left(180°-A\right)$, and $\tan A=-\tan \left(180°-A\right)$ for obtuse angles when $0°\le A\le 90°$
• Establish and apply the relationship $m=\tan \theta$, where $m$ is the gradient of the line and $\theta$ 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.pdf

• 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: $\sin A=\cos \left(90°-A\right)$, $\cos A=\sin \left(90°-A\right)$
• 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