SME
Grade 10 Math · Problem type
Sine and cosine of complementary angles
Use this for “sin 28° is about 0.4695. Which cosine is equal to it?”
Diagram
This page needs a right angle at C.
This is an example. Type your own values to start a new problem.
sin(
A
°)
=
cos(
B
°)
=
s
k
Cosine of B
calculated
Formulas
B
=
90
−
A
62 = 90 − 28
s
=
sin(
A
°)
0.4695 = sin(28°)
k
=
cos(
B
°)
0.4695 = cos(62°)
Assumptions
•
The two acute angles of a right triangle add to 90°: they are complementary.
•
The side opposite A is adjacent to B, so sin A = cos B = cos(90° − A).
•
With a hypotenuse of 1, the side opposite A is sin A.
Step-by-step
WE KNOW
A = 28°
FIND
angle B (B), sine of A (s), cosine of B (k)
Step 1 · Find angle B (B)
Use B = 90 − A
The acute angles of a right triangle add to 90°.
B
=
90
−
28
B
=
62°
Step 2 · Find sine of A (s)
Use s = sin(A°)
The
sine
of
A
:
the
side
opposite
A
over
the
hypotenuse.
s
=
sin(28°)
s
=
0.4695
Step 3 · Find cosine of B (k)
Use k = cos(B°)
The
cosine
of
B
:
the
side
next
to
B
over
the
hypotenuse.
k
=
cos(62°)
k
=
0.4695
Check
Put the numbers back in. Both sides should match.
62 = 90 − 28 ✓
0.4695 ≈ sin(28°) ✓
0.4695 ≈ cos(62°) ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Refresh
Related lessons
Right-triangle trigonometry: sine, cosine and tangent
Main lesson
Find a side from an angle
Use this for “A 7.5 m ladder leans at 38° to the ground. How high up the wall does it reach?”
Find an angle from two sides
Use this for “A ramp rises 1.5 m over a run of 6 m. What angle does it make with the ground?”
Angle of elevation
Use this for “Standing 36 m from a tree, you look up 28° to its top. How tall is the tree?”