Lesson 3 of 5
Use coordinates, reference angles, and quadrant signs for exact trig values.
Subject to changeOptional future study, outside the current course sequence. This lesson and its homework preview are unassigned and may change.
One idea at a time. Try the example, then keep going.
Big ideas · 1 of 8
Big ideas
Do this: Read each idea, then say it in your own words.
On the Unit circleA circle of radius one centered at the origin.Exactly: The points satisfying . At angle , the point is .Mix-up alert: Cosine is the horizontal coordinate; sine is the vertical coordinate.See this in Key words, the terminal point for angle is . The radius is 1, so .
A reference angle is the acute angle between a non-axis terminal side and the x-axis. Use familiar 30-,45-, values and set the signs from the quadrant.
For special angles , the sine values are , and the cosine values reverse that list. Keep exact forms unless rounding is requested.
The tangent ratio is , defined when is nonzero. At and , the unit-circle x-coordinate is zero, so tangent is undefined.
Step-through
Do this: Move through the four steps and check each number.
Find , and .
Whole picture, 4 steps
4 steps. Tap a number or Show me how it works.
Worked example
Do this: Follow each step on paper before reading the result.
Worked example
Do this: Follow each step on paper before reading the result.
Mix-up alert
Do this: Explain the wrong idea and the repair.
Wrong idea: sine is the horizontal coordinate because it is named first in SOHCAHTOA. Repair: on the unit circle the order is ; cosine is horizontal and sine is vertical.
Tip
Do this: Use paper. State the definition before you calculate.
At the top of the unit circle, what are cosine and sine? They are 0 and 1 respectively.
Worked example
Do this: Work on paper and explain each step before checking it.
For the ray through :
Watch
Do this: Watch the public lesson, pause to try a step, then return to your practice.
The linked video is free to watch. The creator may offer optional paid resources; they are not needed for this lesson. If YouTube is blocked, use the lesson notes and worked examples here.
Ready when you are.
Activity 1 of 7 · 0 of 7 activities done
Flashcards
Do this: Say an answer before flipping. Use the hint when needed.
Card 1 of 8
0 Know it0 Still learning
Use then .
On the card: Enter or Space flips. Left and Right move. After revealing, 1 marks Still learning and 2 marks Know it. Tab reaches every control.
What are unit-circle coordinates at angle ?
.
What is ?
.
What is ?
.
What is ?
.
Which trig coordinate is negative in quadrants III and IV?
Sine, the vertical coordinate.
What is in unit-circle coordinates?
when is nonzero.
Where are the unit-circle cosine zeros?
, for integer k.
How does a full turn change sine and cosine?
It does not change them.
True or false
Do this: Decide true or false, then read why.
Self-test
Do this: Work on paper, choose an answer, then read the feedback.
6 questions. One at a time.
Practice, not a grade. No timer. Your best score stays in this browser.
Self-test
Do this: Work on paper, choose an answer, then read the feedback.
6 questions. One at a time.
Practice, not a grade. No timer. Your best score stays in this browser.
Write it
Do this: Write a short explanation, then compare it with the model.
Your answer is not saved anywhere. It disappears when you leave the page.
Write it
Do this: Try the extension on paper, then explain your reasoning here.
Your answer is not saved anywhere. It disappears when you leave the page.
Match
Do this: Choose a word, then choose its meaning.
Connect the ideas
0 / 4 connectedChoose a term, then its meaning. Or drag its grip. Use Tab and Enter or Space; Escape clears.
Subject to changeOptional preview. This page does not mean this homework is assigned. Only turn it in if your teacher asks.
Optional practice preview · 3 points if assigned
Opening your homework…
Practice it: You did 0 of 7 activities.
You decide when you have finished. This is your study progress, not a grade.
Not marked finished yet.
