If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

Trig identities from reflections and rotations

Problem

On the following unit circle, θ is in radians.
A unit circle with an angle from the positive x-axis to a ray labeled theta. The point where the ray intersects the circle is labeled negative 0.42, 0.91 and is in the second quadrant.
Without a calculator, evaluate the following expressions to the nearest hundredth.
ExpressionValue
cos(πθ)
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
cos(2π+θ)
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
Stuck?
Stuck?