SME
Grade 12 Math · Problem type
Inverse cosine
Use this for “Find cos⁻¹(−1/2) in degrees and radians.”
Diagram
arccos(−1/2) = 120°, in 0° to 180°.
This is an example. Type your own values to start a new problem.
cos⁻¹(
x
)
=
A
°
t
The angle in radians
worked out (not typed)
Formulas
A
=
cos⁻¹(
x
)
120 = cos⁻¹(−0.5)
t
=
A
×
π
180
2π/3
=
120
×
π
180
Assumptions
•
cos⁻¹(x) is the one angle from 0° to 180° whose cosine is x (the shaded half).
•
The cosine is one-to-one there, so that is the range; x must be from −1 to 1.
•
A negative x gives an angle past 90°, in the second quadrant.
Step-by-step
WE KNOW
x = −0.5
FIND
the angle (A), the angle in radians (t)
Step 1 · Find the angle (A)
Use A = cos⁻¹(x)
The
one
angle
from
0°
to
180°
whose
cosine
is
x
.
A
=
cos⁻¹(−0.5)
A
=
120°
Step 2 · Find the angle in radians (t)
Use t = A × π/180
A
half
turn,
180°,
is
π
radians:
multiply
by
π
180
.
t
=
120
×
π
180
t
=
2π/3
(≈
2.09)
Check
Put the numbers back in. Both sides should match.
cos(120°) = −0.5 ✓
2π/3
=
120
×
π
180
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.