Chapter 4-5: Exact Values of Sin, Cos, and Tan

Special Right Triangles: ° 30° 1 2 √3 45° 1 1 √2 Remember to use SohCahToa: Evaluate the following: Sin(45°) Cos(π/3) Tan(π/4) Sin(60°) Cos(π/6) Tan(π/6)

Unit Circle Connection: 45° 1 1 √2 (Cos 45, Sin 45) This is the Opposites Theorem This is the Half- Turn Theorem This is the Supplements Theorem

Unit Circle Connection Continued: 30° 2 1 √3 (Cos 30, Sin 30) 60° (Cos 60, Sin 60)

Reference Angles: A Reference Angle is the angle in the triangle that you are referencing before grabbing the coordinates of it’s point on the circle. The only reference angles (other than the ones on the axes themselves) are 30, 45, or 60. (or π/6, π/4, π/3). Reference Angles are ONLY in Triangles that are connected to the horizontal (x) axis!!!

Finding Reference Angles: Find the reference angle for 135° Find the reference angle for 210° Find the reference angle for 300°

Using Reference Angles: 1)Find the reference angle 2)Find the value of the trig function for that angle 3)Check your quadrant and ask what the s-i-g-n should be for where you are in the circle. Examples: Find the sin of 135° Find the cos of 210° Find the tan of 300°

Using Radian Reference Angles: Counting pieces of “pi”…

Finding Reference Angles: Find the reference angle for 3π/4 Find the reference angle for 13π/6 Find the reference angle for 7π/3

Using Reference Angles: 1)Find the reference angle 2)Find the value of the trig function for that angle 3)Check your quadrant and ask what the s-i-g-n should be for where you are in the circle. Examples: Find the sin of 3π/4 Find the cos of 13π/6 Find the tan of 7π/3