A student said that = cos(5/2) has two solutions on the interval [0, 2) because there
are always two solutions when the angle is restricted to a single circle
. Help the student
identify what they did wrong, if anything. Select all that apply.
C. The student is wrong because even though cos(0) = 5/2 could have at most 2 solutions
on [0,2π), the arccosine has at most one solution no
matter what the interval is.
B. The student is wrong. They forgot to check whether there are any solutions at all.
= cos(5/2) would give a solution to cos(0) = 5/2
but this has no solution because
5/2 = 2.5 is bigger than 1. A point on the circle can't
be 250% of the radius to the
right of center.
C. The student isn't wrong a trigonometric equation restricted to [0, 2π) always has 2
solutions.