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Summer 2013
MAC 1114 Trig
1. Find the values of the six trig functions given the
lengths of the sides of a right triangle.
Opp
Hyp
θ
Adj
Review for Test 1
sin θ = Opp/Hyp
cos θ = Adj/Hyp
tan θ = Opp/Adj
csc θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
◦
2. Use the trig functions to solve a right triangle.
See #1. Also use: the sum of all 3 angles is 180 & Pyth. Th.
3. Use your calculator to find the value of a trig
function or inverse trig functions in both radians
and degrees.
Remember to put your calculator in the correct mode for
degrees or radians.
4. Be able to determine the values of the other 5 trig
functions given the value of one of the trig
functions and the quadrant of the terminal side of
the angle in standard position. (Ex. sin(θ) = -2/5
and θ is in Quad III)
This is the reverse of when you are given a right triangle and
asked to find the value of the trig functions (ratios like
opp/hyp). In this problem you have a ratio and have to put the
values onto the triangle. Then you use the Pythagorean
Theorem to find the third side. Now you have a right triangle
with the lengths of all three sides.
From this it’s just a problem like in #1 of this review sheet,
EXCEPT FOR ONE TWIST. YOU NEED TO USE THE
QUADRANT GIVEN TO DETERMINE THE SIGN FOR EACH
OF THE TRIG FUNCTIONS.
5. a.) Find the values of the six trig functions given
the coordinates of a point, P=(a,b), on the
terminal side of an angle in standard position.
a.) Given a point on the terminal side of an angle in standard
position, (a, b), then
cos x = a/r , sin x = b/r , and r = √ a2 + b2
The other trig functions follow from sin x and cos x.
b.) Find the coordinates of a point,
P=(a, b), on the terminal side of an angle in
standard position given the angle and the radius, r
(r = distance the point is from the origin).
6. Be able to solve problems in applied
situations using right triangles.
These two right
triangles share a
hypotenuse.
b.) The coordinates of P=(a, b) can be found by solving:
a = r cos x and b = r sin x
These problems describe a right triangle and will
provide either the lengths of two sides or one side
and one angle. Once you draw the diagram of the
triangle, you can solve the problem using the
definitions given in #1 above.
Some problems require you to solve two triangles
that have a side or an angle in common. Use the
equation from one triangle to substitute for a piece
of information in the other triangle.
This is just 2 right triangles
that share one side.
θ
angle of elevation θ
angle of depression
This is another way that right
triangles can share a side.
Summer 2013
MAC 1114 Trig
Review for Test 1
7. Given one of the special angles (0, 30,
45, 60, 90 or equivalent radian angles
0, π/6, π/4, π/3, π/2 and their multiples),
be able to sketch the angle in an
approximate position (at least in the
correct quadrant) and label its
coordinates on the unit circle.
Know the position of these angles and the
coordinates on the unit circle (a,b) given for each of
these angles which are shown in Fig. 5 on pg 103 of
your text book.
8. Be able to determine (without a
calculator) the values of the six trig
functions for the angles 0, 30, 45, 60,
90 or equivalent radian angles 0, π/6,
π/4, π/3, π/2 and their multiples.
Know the coordinates (a,b) given for each of these
angles in Fig. 5 on pg 102 of your text book. Then
use:
cos x = a and sin x = b.
Pay attention to the sign (+ or -) of a and b!
The rest of the trig functions follow from knowing
the value of cos x and sin x.
Pay attention to the sign (+ or -) of a and b!
9. Know how to solve for arclength, radius
or angle given two of these and/or the
circumference of a circle.
θD = s where C = 2πr and θR = s
360
C
r
10. Be able to convert the measure of an
angle between radians and degrees.
𝜃𝐷
𝜃𝑅
=
180°
𝜋
.
𝑜𝑟 𝜃𝐷 = 𝜃𝑅
180°
𝜋
.
𝑜𝑟 𝜃𝑅 = 𝜃𝐷
𝜋
180°
Review Problems for Test 1
1 – Ch 1 Rev – 10, 18
6 – Sec. 1.4 – 1*, 3*, 5*, 13, 15*,39, 43
Ch 1 Rev –31, 35, 38, 40
2 – Ch 1 Rev - 11, 23
7 – Ch 2 Rev – 1, 2, 4, 15
3 – Ch 2 Rev - 11, 12
4 – Ch 2 Rev – 48, 50
Sec 2.3 – 17*, 19*, 21, 23, 51*, 53*, 55*
5 – Ch 2 Rev - 8
Sec 2.3 – 11*, 13*, 15*, 47*, 49
8 – Ch 2 Rev – 14, 34-42, extra practice
49,51,52
9 – Ch 1 Rev – 26
Ch 2 Rev – 19, 53
10 – Ch 2 Rev – 5, 21
*These problems were assigned as regular homework.