Download math 105 – study guides

MATH 105 – STUDY GUIDES
Section 6.1
Look at the exercises in section 6.1 and you will find problems of the types listed below. These are the
types of problems you need to master. On the back of this page you may write the procedures
1)
2)
3)
4)
5)
6)
7)
Definitions of the six trigonometric functions
Given a triangle with labeled sides, give the trig functions of the acute angles
Given the value of a trigonometric function, find reciprocal angle values
Know the values of the trigonometric functions of the angles 30, 60 and 45 degrees
Convert an angle from degrees to degrees, minutes and seconds
Convert an angle from degrees, minutes and seconds to degrees
Use the calculator to find the trig functions of acute angles (What do you do when you don’t have the
specific key that you need? Ex: find the cot (72 degrees))
8) Use the calculator to find an angle when the trigonometric function of the angle is given
(What you do when you don’t have the specific key that you need? Ex: find the angle A if cot A =
2.345))
9) Relations between the trig functions of complementary angles (Functions = CO functions of the
complement)
10) Given one trigonometric function of an acute angle, find all others (Steps: sketch triangle, label, find the
missing side with Pythagorean theorem and then find the functions)
11) Solve right triangles: find all angles and sides of a right triangle if they give you
a) An angle and a side, or
b) Two sides
Section 6.2
12) Solving right triangles – applications
o Read the problem, think on the situation
o Sketch the right triangle that represents the situation
o Put the given information in the graph
o Put the missing information in the graph using a variable
o Think what trig function relates the given info with the missing info
o Use that trig function to write the equation
o Solve the equation showing all steps
13) Solving right triangles involving angle of elevation
14) Solving right triangles involving angle of depression
Section 6.3
15) Be familiar with the vocabulary
o Angle in standard position
o Positive and negative rotation
o Initial side
o Terminal side
o Coterminal angles
o Reference angle
o Supplementary angles
o Quadrantal angles
16) Know the values of quadrantal angles
17) For any given angle, indicate in which quadrant is the terminal side
18) Give values of coterminal angles in positive and negative directions
19) Find the complement of an angle (with degrees, minutes, seconds)
20) Find the supplement of an angle (as above)
21) Given the coordinates of a point which is on the terminal side of an angle, find the trigonometric
functions for the angle (#25-28)
22) Sketch an angle in the correct quadrant and find the reference angle
23) Sketch an angle in the correct quadrant and determine the signs of trigonometric functions
24) Find trigonometric functions of special angles in different quadrants – without the calculator –
suggested steps follow:
a) Sketch the angle in the correct quadrant
b) Project towards the x-axis
c) Find the value of the reference angle
d) Think on the sign of the trigonometric function (put + and – on the sides of the triangle)
e) Use the value of the reference angle to finish
25) Find trigonometric functions of any angle – with the calculator
26) Given the trig functions of any angle, (let’s say 40D), find the trig functions of another angle in another
quadrant that has the given angle as reference angle (let’s say 140D, or 220D, or 320D, or -400D) (#8588)
27) Given the value of a trig function of an angle and the quadrant in which the terminal side is, find all
other trig functions
Section 6.4 (study problems 1-48 only, the other topics from this section will not be studied)
28) Sketch a unit circle and mark the points determined by the given real numbers (angles given in radians)
(#1-6 in book)
29) From a graph, to a real number (to an angle given in radians) (#7, 8)
30) Convert angles from degrees to radians in terms of pi (this is the exact form)
31) Convert angles from degrees to radians - do not leave answers in terms of pi (write as decimals, this is
the estimate)
32) Convert angles from radians to degrees
Section 6.5 – in the test we’ll cover the following
33) Find the trig functions of the angles given in radian – give answers in exact form (# 1-16 and 49-62)
34) Find the trig functions of angles given in radian – use the calculator (here you have to press the MODE
key and select radian mode) (# 17-32)
35) Find the other function values given certain conditions (# 71-80)
36) The graphs from these section will be given as an assignment