#MeasurementAndSpace #Path #Adv
>[!info]- [Trigonometry D (Path) | NSW Curriculum Website](https://curriculum.nsw.edu.au/learning-areas/mathematics/mathematics-k-10-2022/content/stage-5/fa632cab9d)
>- MA5-TRG-P-02 establishes and applies the properties of trigonometric functions and finds solutions to trigonometric equations
## 📖 Prior Knowledge
| Content | Prior knowledge | Used for |
| ------------------------------ | ------------------ | ------------------------------------------------------ |
| [[Linear Relationships C]] | - gradient formula | - tan and gradient |
| [[Functions and other Graphs]] | - functions | - reconceptualising trigonometric ratios as a function |
| [[Trigonometry C]] | - sine rule | - 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) $0°≤\theta≤360°$, 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 $\sin A=\sin\left(180\degree-A\right)$, $\cos A=-\cos\left(180\degree-A\right)$, and $\tan A=-\tan\left(180\degree-A\right)$ for obtuse angles when $0\degree\le A\le90\degree$
- 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:Â $\sin A=\cos\left(90\degree-A\right)$, $\cos A=\sin\left(90\degree-A\right)$
- 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