Lesson 5 of 5
Isolate one trig function and find every angle in the stated interval.
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Big ideas
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A linear trig equation such as is solved first with algebra: . This lesson uses one unsquared trig function, without products of trig functions.
A solution interval controls which angles to keep. includes 0 and excludes ; uses degree answers.
A reference angle gives a magnitude; the trig sign tells you the possible quadrants. Sine is positive in I and II, cosine positive in I and IV, and tangent positive in I and III.
The range of sine and cosine is , so a target outside it gives no real solutions. Tangent is undefined at for integer k. Substitute candidates in the original equation and keep only interval members.
Step-through
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Solve for .
Whole picture, 4 steps
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Worked example
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Worked example
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Mix-up alert
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Wrong idea: the first calculator angle is the complete solution set. Repair: check the other matching quadrant and periodic copies in the stated interval. Also reject any target outside the sine or cosine range.
Tip
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On , explain why both 0 and can have the same coordinates while only one is in the interval.
Worked example
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Solve on .
Watch
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Flashcards
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Card 1 of 8
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Use algebra before searching for angles.
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What is the first step for ?
Isolate .
Which quadrants have positive sine?
I and II.
Which quadrants have negative cosine?
II and III.
Which quadrants have positive tangent?
I and III.
What are sine and cosine ranges?
.
What is the tangent period?
radians or .
What does exclude?
The endpoint .
How do you verify an angle solution?
Substitute it into the original equation and check interval and domain.
True or false
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Self-test
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6 questions. One at a time.
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Self-test
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6 questions. One at a time.
Practice, not a grade. No timer. Your best score stays in this browser.
Write it
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Write it
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Match
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Connect the ideas
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