Learn with Amar
Teaching video
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Grade 11 chapters and video availability01 · Read and understand
What you will learn
- Apply an angle-addition identity instead of rounding early.
- Justify the conclusion "sin75°=(√6+√2)/4" using the stated assumptions.
Before you start
Exact values at 30°,45°,60°.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
Find sin 75° exactly.
Why this math matters
Apply an angle-addition identity instead of rounding early. This worked micro-lesson connects a precise mathematical condition to a conclusion you can check. The transfer task asks you to change the setting and decide which parts of the reasoning still apply.
Set up the model
A useful answer starts with clear assumptions:
- Angles are stated in degrees in this lesson.
- The standard addition identities apply.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Find an exact trigonometric value from familiar angles
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Find sin 75° exactly.
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Build the model
75°=45°+30°
The sum uses two angles with known exact values.
Work through the mathematics
sin75°=sin45°cos30°+cos45°sin30°
The sine addition identity contains two products.
Check the conclusion
sin75°=(√6+√2)/4
Substituting the exact radicals preserves the exact answer.
The result
sin75°=(√6+√2)/4
Substituting the exact radicals preserves the exact answer.
Common mistakes to catch
- The cosine addition formula uses a minus sign between products.
- A sum inside a sine cannot be separated into a simple sum of sines.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
Find cos75° exactly.
Show a hint
Use the cosine addition identity and its minus sign.
Reveal answer and explanation
(√6−√2)/4
√2√3/4−√2/4 gives the result.
Practice 2
Is sin(a+b)=sin a+sin b a valid general identity?
Show a hint
Test a=b=30°.
Reveal answer and explanation
No
sin60°=√3/2 differs from one.
Take the idea with you
Combine calibrated angle components while keeping exact symbolic values.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Keep quadrant information in a double-angle calculation
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