Ch 4 test tomorrow 2/18
4.2: finding trig ratios given a triangle, word problems
4.3: terminal side, reference angle (reference triangle), quadrantal angle, find trig ratios given 2 conditions (ex: tan
= 9/5 and cos < 0), finding an angle in radians knowing the unit circle (answer in radians)
4.4 & 4.5: determine amplitude, period, & frequency of a sinusoid, graph a parent function & its transformation
4.7: Inverse functions – using the calculator and by hand
4.8: word problems – these will include angle of elevation & depressions, as well as finding the angle measure
**Unless otherwise stated all angle answers need to be in radians**
Review Part 1: calculator part
In degrees:
1. arcsin .34
2. tan-1 3.4
In radians:
3. arcos -.4
4. sin-1 .8
5. You are 6 feet tall and are looking at the top of a tree at an angle of 15°. If you are standing 100 feet from
the tree, how tall is the tree?
6. An entrance ramp to an interstate is 455 feet long. The ramp rises 200 feet from the ground to the top of
the ramp. What is the angle that the ramp makes with the ground?
Part 2: non-calculator part
1. P (5, -2) is the terminal side. Evaluate all 6 trig ratios
sin =
2. Evaluate using reference angle (remember you will be drawing a 45-45-90 or 30-60-90 triangle, so
remember your standard reference triangles – 1,1,
a. cos
and 1,
= 1/2
b. cot 120 =
3. Using quadrantal angles find the sin, cos, and tan of
(remember these will always be at 0, 90, 180, or
270 so you need to use the points: (1, 0),(0, 1), (-1, 0), or (0, -1), sin is always the y-coordinate, cos is always
the x-coordinate, and tan is always y/x)
sin
= 1, cos
= 0, tan
=ø
4. Find trig ratios given 2 conditions:
Find sin and cos when cot
Since cot
is negative in quadrant 2 & 3, draw your triangle in
quadrant 3 (since that is the only quadrant they have in common)
sin
5. Using what you know about unit circles, find a unique # that is between 0 and 2 that satisfies the
following conditions:
a.
:
b.
6. Find the amplitude (|a|), period (
, and frequency (
for the following:
a. f(x) = -4sin (x – 3): A: 4, P:
b. f(x) = cos (2x) + 1: A: 1, P:
7. graph
a. f(x) = sin (x – 1) + 2
the darker graph is sin x, the lighter one is the transformation
Transformation: right 1, up 2
b. f(x) = 1/2cos(x + 2) – 1
the lighter graph is cos x, the darker graph is the transformation
Transformation: left 2, down 1, shrink ½ (that means the amplitude is now ½ instead of 1)
8. solve for x in a given interval using reference triangles
csc x = 2,
draw your triangle in quadrant 2, label the sides and then decide your reference angle, since you’re in
quadrant 2 to find your answer take 180-reference angle, and then convert to radians
1
2
so 30° is opposite of 1, 180-30 =150° =
-
9. use inverses
a. arcsin (
=
b. tan-1 (
c. sin-1(1) =
d. sin (tan-1
e. cos-1 (sin
= cos-1 1 = 0
f. sin-1 (tan
= sin-1
= -1