Download Practice Problems

Name
Review Chapter 9 - Graphing, Inverse Trig
Functions and Solving Trig Equations
1. Determine an equation for each of the trig graphs shown below.
a.
d.
b.
c.
e.
2. In the interval, 0 <  < 2, graph y = 2cos½ and y = tan. State the number of
times 2cos½ = tan. State TWO of the points of intersection of the two graphs. If
necessary, round the coordiantes of the point(s) of intersection to the nearest
thousandth.
3. State the amplitiude, frequency, period, and the range of y = -5sin( ¼x) + 9.
4. On the grid provided, graph one period of y = 3sin2.
5. In the interval 0 <  < 2, graph the equation y = 4sin( - ). Write an alternate
equation to represent the graph.
6. State all value of arcsin ( ½ ) such that 0 < θ < 360.
7. Evaluate: cos (arcsin 6/7)
8. In the interval –π <  < , graph the equation y = - 3cosx + 5.
9. Evaluate and express your answer in radians:
a. Arcsin (- ½ )
b. Arccos( - 3)
2
10. In the interval 0 <  < 2, graph the equation y = 2sec
11. A small toy attached to the end of a slinky (or spring) goes up and down according to an
equation of the form y = a sin(bx). The motion of the toy starts at rest, goes up to its highest
position of 5 inches above its rest point, bounces down to its lowest position of 5 inches
below its rest point, and then bounces back to its starting place in a total of 4 seconds. Write
an equation that represents this motion. Graph your equation from x = 0 seconds to x = 12
seconds.
12. State the amplitiude, frequency, period, domain and range of y = 2sin(4x) – 5.
13. In the interval – <  < , graph y = 3csc.
14. Evaluate, in terms of x:
cos(arctan 4 )
3x
15. Solve for all values of θ, such that 0 ≤ θ ≤ 360 - round to the nearest tenth of a degree
when necessary.
8sin2θ - 5 = sin2θ - 2
16. Solve for all values of θ, such that 0 ≤ θ ≤ 360 – round to the nearest degree when
necessary.
5sin2θ – 7cosθ + 1 = 0
17. Solve for all values of θ, to the nearest hundredth of a degree, such that 0 ≤ θ ≤ 360.
2cos2θ – 3sinθ = 1
18. Solve for all values of θ, to the nearest thousandth of a degree, such that 0 ≤ θ ≤ 360.
5 = 4cos2θ + 2
19. Solve for all values of x such that 0 ≤ x ≤ 2π.
3cosx + sin 2x = 0
20. The horizontal distance, in feet, that a golf ball travels when hit can be determined by
the formula
d = v2sin2θ
g
where v equals initial velocity, in feet per second; g equals
acceleration due to gravity, θ equals the initial angle, in degrees, that the path of
the ball makes with the ground; and d equals the horizontal distance, in feet,
that the ball will travel.
A golfer hits the ball with an initial velocity of 180 feet per second and it travels a
distance of 840 feet. If g = 32 feet per second per second, what is the smallest initial
angle the path of the ball makes with the ground, to the nearest degree?