SME
Grade 11 Math · Problem type
Degrees and radians
Use this for “Convert 225° to radians” or “Convert 7π/6 to degrees.”
Diagram
θ
=
5π/4:
the
point
(cos
θ,
sin
θ)
is
(−
√
2
2
,
−
√
2
2
).
Reference angle: π/4.
This is an example. Type your own values to start a new problem.
d
°
=
p
q
π
g
Greatest common factor of d and 180
calculated
Formulas
g
=
GCF(
d
,
180)
45 = GCF(225, 180)
p
=
d
g
5
=
225
45
q
=
180
g
4
=
180
45
Assumptions
•
180° = π radians, so d° is d/180 of π; write the fraction in lowest terms.
•
One radian is the angle whose arc equals the radius.
•
Going back, pπ/q is p × (180 ÷ q) degrees: 7π/6 = 7 × 30° = 210°.
Step-by-step
WE KNOW
d = 225°
FIND
greatest common factor of d and 180 (g), top of the fraction of π (p), bottom of the fraction of π (q)
Step 1 · Find greatest common factor of d and 180 (g)
Use g = GCF(d, 180)
d
°
is
d
180
of
π:
the
greatest
common
factor
puts
d
180
in
lowest
terms.
g
=
GCF(225,
180)
225
×
π
180
=
225π/180
g
=
45
Step 2 · Find top of the fraction of π (p)
Use p = d ÷ g
Divide
the
top,
d
,
by
the
common
factor.
p
=
225
45
p
=
5
Step 3 · Find bottom of the fraction of π (q)
Use q = 180 ÷ g
Divide the bottom, 180, by the common factor.
q
=
180
45
225° = 225π/180 = 5π/4
q
=
4
Check
Put the numbers back in. Both sides should match.
45 = GCF(225, 180) ✓
5
=
225
45
✓
4
=
180
45
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Refresh
Arc length, sector area and radian measure
The Pythagorean theorem's converse and special right triangles