Download test four

Mathematics 120 test four
Thursday, March 18, 2004
(1) Convert 120◦ to radians.
(2) A central angle A intercepts an arclength s = 7 from a circle of radius r = 5. (see
picture) Find the radian and degree measure of the angle A.
(3) An central angle θ inside a unit circle is sketched below. Use the data to find exact
values for
cos θ =
sin θ =
tan θ =
sec θ =
csc θ =
cot θ =
(4) If cos B = − 25 and B is in quadrant three, find exact values (involving square roots when
necessary) for
sin B =
(5) Show that
tan θ + sec θ
sin θ + 1
=
1 + sec θ
cos θ + 1
tan B =
page two
(6) If θ = sin−1 m, then sin
=
and θ is between
and
.
(7) Find the exact values (involving square roots when necessary):
cos
π
6
=
tan (60◦ + k · 180◦ ) =
(8) Use an angle subtraction formula to expand & simplify the quantity 8 cos θ −
(Your answer will have the format a cos θ + b sin θ)
(9) If x = 3 tan θ and θ is in quadrant 4, simplify the quantity
√
9 + x2
π
3
page three
(10) Simplify each expression below:
(a) sin sin−1 m =
(b) cos sin−1 m =
(11) Decide whether each of the following statements is true or false:
• for any angle θ, sin 2θ = 2 sin θ.
• for any second quadrant angle A and associated reference angle Ar , sin A = sin Ar .
• for any angle θ in the domain of sec, sec(θ + π) = sec θ.
• for any angle θ in the domain of csc, csc(−θ) = − csc θ.
• Of the six graphs of the trig functions sin, cos, tan, csc, sec, and cot, exactly four of
the graphs have vertical asymptotes.
(12) Sketch a graph of the function y = 5 cos 8x −
The graph should show all quarter-cycle points.
π
.
3
page four
(13) Find all solutions θ, 0 ≤ θ < 360◦ for each trigonometric equation below: (round to the
nearest degree)
(a) tan θ = − 47
(b) sin 2θ =
5
6
(14) Given the sinusoidal graph below, find the function’s
period =
amplitude =
frequency =
horizontal shift =
angular frequency =
function’s equation: y = A sin(Bx + C) (what are A, B, & C) ?