Week 17 – Pre Calc 11 – Rotational vs Reference Angles

This week in Pre Calc 11 we continued our learning of trigonometry and were talking about rotational angles and their significance when plotting a triangle on the cartesian plane, one of the key takeaways from this week was that calculators are dumb and you need to remember that sometimes it will give you a reference and sometimes it will give the rotational angle depending on which ratio is used and if the ratio is positive or negative

for example a question said cos Θ = – and i went through and did the equation to solve for Θ and came up with () (-) and when i plugged it into my calculator i got an angle of about 84 degrees so i put it in quadrant one and called it a day, what i didnt think about at the time was that the original equation had stated that cos was negative meaning that the angle can only be in quadrant 2 or 3 making 84 a reference angle and the actual angles being 96 or 264

it is important to know how to tell if an angle is a rotation angle or a reference angle with a unit as calculator heavy as trig because the calculator will just give you a reference angle usually and you will need to determine which quadrants the angle resides in and then determine the angles