Mathematician _____________________________________________ Date __________
General info
You will get another copy of the formula sheet.
There will only be a few problems that require the use of a calculator.
Your test is not limited only to items on this review sheet. Make sure that you complete the chapter
review questions in the textbook and look through all lessons in Chapter 7.
Trig identities and equations
Things to memorize/know:
 sin 2q + cos2 q = 1
 How to use sin 2q + cos2 q = 1 when establishing identities and solving tri equations.

How to use sin 2q + cos2 q = 1 to find identities involving the other trig functions.
sinq =
cosq =


How to find angles in radians using your calculator for Quadrants II, III, IV
Properties of inverse functions- especially take note of the restrictions!
o
sin -1 , cos-1 , tan -1
csc -1 , sec -1 , cot -1
Proving identities – Focus on applying your algebra skills using trigonometric expressions, e.g. factoring,
finding common denominators, etc. Remember that in this kind of problem you should move from the
LHS to the RHS (or vice versa), and that you CANNOT do any operations that change both sides at once,
e.g. adding/subtracting/multiplying/dividing both sides by the same thing, or cross-multiplying.
1.
Establish the identity
sin 2x
= tan x
1 + cos 2x
Sum-and-difference, double-angle, half angle identities – One very common type of problem in this section
requires you to draw right triangles in the different quadrants. Remember in this kind of problem that the
hypotenuse is always considered to be positive, but that the other sides can be negative, depending on the
quadrant. Additionally, you must also be able to identify what quadrant your answer is in- half angle
identities require you to do this since the square root can be positive or negative.
1
3p
3
p
2. If sin A = - , p < A <
, and cos B = , 0 < B < , find the value of
4
2
4
2
(a) cos ( A + B )
(b) sin 2A
æ Aö
(c) sin ç ÷
è 2ø
æ Bö
(d) cos ç ÷
è 2ø
Other common problems for identities
 Finding exact function values
3. Find the exact value of sin
rationalize denominators.]

11p
. [Note: Exact value means no decimals. Leave square roots but
12
Establishing identities
pö
æ
4. Establish the identity cos ç x + ÷ = - sin x
è
2ø
Trig equations -- This is another reason to review/make sure you know the unit circle! Make sure you look
over:
 Problems where the angle is not just  or x.
pö
æ
5. Solve 4 sin ç 3x + ÷ + 8 = 0 for 0 £ x < 2p .
è
2ø

Quadratic-type equations, with or without identities.
6. Solve 3sin x + cos2x = 2 for 0 £ x < 2p .

Calculator equations using reference angles.
7. Solve for 0 £ x < 2p . Give your answers in radians rounded to the nearest hundredth.
(a) tan x =
1
5
(b) sin x = -
2
5
Trig Inverse Functions and Graphs( go back to 7-1 and 7-2)
Thinking about the graphs and properties of basic inverse functions may help you remember their
properties.
(a) y = sin-1 x
(b) y = cos-1 x
(c) y = tan-1 x
Domain:
Domain:
Domain:
Range:
Range:
Range:
Then make sure you know how to:
 Use the domain and range of the inverse trig functions to answer questions like:
8. What is the value of
æ
3ö
-1
(a) cos ç ÷
è 2 ø
1ö
æ
csc ç tan -1 ÷
(c)
è
2ø
(
-1
(b) tan - 3
)
é
æ
3öù
cot ê cos -1 ç ÷ú
(d)
è 3 ø ûú
êë