Discover double angles (AASL 3.6)
Keywords
| Double Angle Formulas | 二重角公式（にじゅうかくこうしき） | 双角公式（shuāng jiǎo gōng shì） | 이중 각도 공식 (i-jung gakdo gongsik) |
| Sine | サイン（さいん） | 正弦（zhèng xián） | 사인 (sain) |
| Cosine | コサイン（こさいん） | 余弦（yú xián） | 코사인 (kosain) |
| Tangent | タンジェント（たんじぇんと） | 正切（zhèng qiè） | 탄젠트 (tanjenteu) |
| Trigonometric Functions | 三角関数（さんかくかんすう） | 三角函数（sān jiǎo hán shù） | 삼각 함수 (samgak chuso) |
| Trigonometric Identities | 三角関数の恒等式（さんかくかんすうのこうとうしき） | 三角恒等式（sān jiǎo hán děng shì） | 삼각함수 정체성 (samgakhamsoo jeongchejung) |
| Pythagorean Identity | ピタゴラスの定理（ぴたごらすのていり） | 勾股定理（gōu gǔ dìng lǐ） | 피타고라스 정리 (pitagoras jeongri) |
Inquiry questions
| Factual Inquiry Questions What are the double angle formulas for sine, cosine, and tangent? How can the double angle formulas be derived from the sum of angles formulas (HL)? | Conceptual Inquiry Questions Why are double angle formulas important in simplifying expressions involving trigonometric functions? How can double angle formulas be used to solve trigonometric equations that involve squared terms? | Debatable Inquiry Questions Is the use of double angle formulas more efficient than other trigonometric identities in solving complex trigonometric problems? |
Step 4: Identify the Formulas - Using the matches you've made, try to identify the expressions that seem to involve doubling an angle. Question 2: Which expressions could represent the double angle formulas? Hint: Look for expressions where the angle is doubled (like) and try to match them with their equivalent forms.
Step 5: Explore the Pythagorean Identity - Which expression from the applet adds up to .They are linked to a famous trigonometric identity. Question 3: Which expression pairs add up to ? How do they demonstrate the Pythagorean identity ? By considering a right triangle with hypotenuse can you prove this identity?
Step 6: Confirm Your Findings - Use a calculator to confirm the equivalences you've found. Do the values agree with your predictions? Step 7: Reflection - Reflect on how the expressions relate to the double angle formulas and the Pythagorean identity. Question 4: Can you write down the double angle formulas for sine and cosine using the expressions you've matched?
Part 2 - Checking for understanding
If , what is ?
If , what is ?
Given , what is ?
Part 3 - Exam style questions
[MAA 3.6] TRIGONOMETRIC EQUATIONS
![[MAA 3.6] TRIGONOMETRIC EQUATIONS.pdf](https://www.geogebra.org/resource/rn3afajg/gMlLEdk4XaaPViG3/material-rn3afajg-thumb.png)
[MAA 3.6] TRIGONOMETRIC EQUATIONS_solutions
![[MAA 3.6] TRIGONOMETRIC EQUATIONS_solutions.pdf](https://www.geogebra.org/resource/fqt6zesm/ccj0oqDuKyN9NPUN/material-fqt6zesm-thumb.png)
Optional extension
Why does ?
Why is ?
Why does ?
Why does ?
In question 3 you explained why . Why is it also true that ?
Explain why is ?
