5-3 Solving Trigonometric Equations Worksheet With Answers Page 5
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28On the interval [0, 2π), the equation cos x = 1 has a
solution of 0 and the equation cos x = –1 has a
5-3 Solving Trigonometric Equations
solution of π.
2
The interval is [15.4°, 74.6°].
18.
2 sin
x = sin x + 1
SOLUTION:
b.
On the interval [0, 2π), the equation sin x = 1 has a
solution of
and the equation sin x =
has
solutions of
and
.
If the distance to the net is 50 feet, then the angle
19.
would be 19.9° or 70.1°.
TENNIS A tennis ball leaves a racquet and heads
toward a net 40 feet away. The height of the net is
20.
SKIING In the Olympics aerial skiing competition,
the same height as the initial height of the tennis ball.
skiers speed down a slope that launches them into
the air, as shown. The maximum height a skier can
reach is given by h
=
, where g is
peak
the acceleration due to gravity or 9.8 meters per
second squared.
a. If the ball is hit at 50 feet per second, neglecting
air resistance, use
to find the
interval of possible angles of the ball needed to clear
the net.
b. Find
if the initial velocity remained the same
a. If a skier obtains a height of 5 meters above the
but the distance to the net was 50 feet.
end of the ramp, what was the skier’s initial speed?
b. Use your answer from part a to determine how
SOLUTION:
long it took the skier to reach the maximum height if
a.
t
=
.
peak
SOLUTION:
a.
The interval is [15.4°, 74.6°].
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Page 5
The skier’s initial speed was 11.67 meters per
b.
second.
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