That's not what they want.
When it says "exact" values, you need answers that are either
rational numbers of results expressed as square roots, etc
These kind of questions usually involve standard angles, that is,
angles whose trig ratios you should know
You must also know the patterns of the CAST rule.
Some people have an easier time thinking in terms of degrees vs radians
e.g. (a) tan(5π/6) = ??
is the same as tan(150°)
and 150° has 30° as its angle in standard position
You must know tan 30° = 1/√3
and since 150° is in quadrant II, and by the CAST rule the tangent is
negative in quad II
tan 150° = -1/√3
tan(5π/6) = -1/√3 or -√3 / 3 if you need it rationalized.
one more:
csc(3π/4)
= csc 135° , in quad II where the sine and cosecant are positive
= + csc 45°
= 1/sin 45° = 1/(1/√2)
= √2
Evaluate each of the following. Leave results as exact values.
(a) tan(5π/6) =
(b) tan(4π/3) =
(c) cot(7π/4) =
(d) sec(2π/3) =
(e) csc(3π/4) =
My answers
(a) tan(5π/6) = -.577350
(b) tan(4π/3) = 1.732051
(c) cot(7π/4) = -1
(d) sec(2π/3) = -2
(e) csc(3π/4) = 1.414214
3 answers
They do want it in exact form though
I submited it and 40% was right
I submited it and 40% was right
They should not have accepted those answers, except c) and d)
or else drop the "exact" answer request.
or else drop the "exact" answer request.