Quadrant — Grade 6 Math, what it means and where it is taught
One of the four regions the axes divide the plane into.
Taught in Grade 6 Math.
Where it is taught
Practise this idea
11 questions in the course bank use Quadrant, in Radians & the Unit Circle, Trigonometric Identities & Equations, Inverse Trigonometric Functions, Polar Coordinates, The Coordinate Plane. The first 8 are below; the rest are in those units.
Problem 1
In quadrant III, which is true?
- Both sine and cosine are negative
- Sine positive, cosine negative
- Both positive
- Sine negative, cosine positive
Worked answer
Both sine and cosine are negative
Quadrant III has x<0 and y<0
cos follows x, sin follows y
Problem 2
If sinθ=35 and θ is in quadrant II, find cosθ.
Worked answer
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Problem 3
Solve sinθ=12 for 0° ≤ θ < 360°. Give both answers, smallest first.
Worked answer
30,150
Reference angle 30°
30° and 180-30=150°
Problem 4
Solve cosθ=12 for 0° ≤ θ < 360°. Give both, smallest first.
Worked answer
60,300
Reference angle 60°
60° and 360-60=300°
Problem 5
How many solutions does sinθ=0.4 have for 0° ≤ θ < 360°?
Worked answer
2
One in quadrant I, one in quadrant II
Problem 6
Find arccos(-12) in degrees.
Worked answer
120
Reference angle 60°
Cosine is negative in quadrant II, so 180-60=120
Problem 7
For the point (-2, -2), find θ in degrees with 0° ≤ θ < 360°.
Worked answer
225
tanθ = 1 gives 45°
Quadrant III, so add 180°: 225°
Problem 8
In which quadrant is (3, 5)?
- I
- II
- III
- IV
Worked answer
I
Right and up is quadrant I