Given One Trig Function, Find Others Write definitions of given and needed functions. Use Pythagorean Theorem to find missing side. adjacent hypotenuse opposite x˚
Angles in Standard Position Vertex is always at the origin. Initial side is always on the positive x axis. Terminal side is the ending side.
Angles in Standard Position Positive angle = counterclockwise 0˚ 90˚ 180˚ 270˚
Angles in Standard Position Negative angle = clockwise 0˚ −270˚ −180˚ −90˚
Angles in Standard Position Quadrantal angle = angle not in a quadrant: 0˚, 90˚, 180˚, 270˚, 360˚, etc. Quadrantal angles will not use reference angles.
Coterminal Angles Coterminal angles always differ by a multiple of 360. Every angle has an infinite number of coterminal angles. The interval given determines how many and which coterminal angles may be used.
Reference Angles All reference angles are acute. An acute angle does not need a reference angle (or is considered its own reference). Quadrantal angles NEVER use reference angles.
Reference Angles for Angles > 360˚ If the given angle is greater than 360˚, first find a coterminal that falls in the interval 0˚≤ x < 360˚. Now find the reference angle based upon the coterminal angle.
Reference Angles for Angles < 0˚ If the given angle is negative, first find a coterminal that falls in the interval 0˚≤ x < 360˚. Now find the reference angle based upon the coterminal angle. Remember: What is true about ALL reference angles?
Trig With Reference Angles If angle given is not acute, first find the reference angle. Consider whether the trig function is positive or negative in this quadrant. Find answer based upon showing these two pieces of information.