Without using a calculator, compute the sine and cosine of (7π) /4 by using the reference angle.

Question

Without using a calculator, compute the sine and cosine of (7π) /4 by using the reference angle.

What is the reference angle? ____ radians

In what quadrant is this angle? ___

sin (7π) /4 =

cos (7π) /4 =

Answer 1

π7/4 is the same as -π/4. This is in Quadrant IV. For QIV cos(-x) = cos(x), so this is the same for cos(π/4).

cos(π/4) = √2/2.

sin(7π/4) = sin(-π/4). For QIV, sin(-x) = -sin(x) = -√2/2