Co-functions
Co functions
Co-functions:
Two functions whose angles are complements.
Examples:
sin 60 = cos 30
sec 45 = csc 45
tan 60 = cot 30
1
Therefore:
The prefix co- allows you to
identify pairs of cofunctions:
Sine and Cosine
Tangent and Cotangent
Secant and Cosecant
Notice that the prefix
co- is also used in
complementary.
Examples
Ex 1) Angles A and B are the acute angles in a
2
5
right triangle. If sin A = , find the
cosB , using co-functions.
Using co-functions,
‫࡮ ܛܗ܋ = ࡭ ܖܑܛ‬
cos ࡮ =
૛
૞
2
Examples
Ex 2) Angles A and B are the acute angles in a
1
3
right triangle. If csc A = − , find the
secB , using co-functions.
Using co-functions,
‫࡮ ܋܍ܛ = ࡭ ܋ܛ܋‬
‫ = ࡮ ܋܍ܛ‬−
૚
૜
Examples
Ex3) Angles A and B are the acute angles in a
5
right triangle. If cot A = −
, find the
2
tan B , using co-functions.
Using co-functions,
‫࡮ ܖ܉ܜ = ࡭ ܜܗ܋‬
‫ = ࡮ ܖ܉ܜ‬−
૞
૛
3
More Examples: Solve for a.
(a) sec(9 − 3a ) = csc(47 − a )
Since secant and cosecant are
co-functions, the angles are
complementary (add to 90).
More Examples: Solve for a.
(b)
tan(a + 8) = cot(90 − 2a )
4
More Examples: Solve for a.
(c)
cos(a + 10) = sin(3a + 8)
More Examples using Co-Functions
Ex1) Express sin 285° as the
function of an angle whose
measure is less than 45°.
5
Steps:
1. Determine the quadrant.
Quadrant IV
2. Determine the reference angle.
Reference Angle= ૠ૞°
3. Determine if the
function is + or -.
Sine is negative in Quadrant IV
4. Use co-functions to re-write
the function.
−‫ ܖܑܛ‬ૠ૞° = −‫ ܛܗ܋‬૚૞°
2. Express cot 87°20’ as a function of
an acute angle whose measure is less
than 45°.
Step 1: Determine the quadrant.
Quadrant I
Step 2: Determine the reference angle.
Reference Angle= 87°*′
Step 3: Determine if the function is + or -.
Cotangent is positive
Step 4: Use co-functions to re-write
the function.
cot ,(°*′ = !" °-*′
6
Example:
3. Rewrite each function in terms of its co-function.
Then, find the value of co-function to four decimal
places.
(a)sec 75° = °
= . ,.-
(b)sin 295° = − .°
= − °
= −. 0*.
7