Use the cofunction identities to write an expression that is equivalent to each of the following expression.
a) sin(pi/6)
sin=cos(pi/2 - pi/6)
What do I do next?
what is π/2 - π/6 ??
= 3π/6 - π/6 = 2π/6 = π/3
so sin(π/6) = cos(π/3)
check:
sin(π/6) = sin 30° = 1/2
cos(π/3) = cos 60° = 1/2
All is good!
Next, you can simplify the expression by applying the cofunction identity for sine and cosine. Since the cofunction of an angle is equal to the sine of its complementary angle, you can rewrite the expression as:
sin(pi/6) = cos(pi/2 - pi/6) = cos(pi/3)
So the expression that is equivalent to sin(pi/6) using the cofunction identity is cos(pi/3).
Next, you need to simplify the expression by using the cofunction identity for sine and cosine. According to the cofunction identity, sin(theta) is equal to cos(pi/2 - theta).
Therefore, sin(pi/6) can be written as cos(pi/2 - pi/6).
Now, you need to simplify the angle inside the cosine function. Since pi/2 - pi/6 equals pi/3, you can rewrite the expression as cos(pi/3).
So, an expression equivalent to sin(pi/6) using the cofunction identity is cos(pi/3).