SAT SUBJECT TEST MATH LEVEL 2
PART 2
REVIEW OF MAJOR TOPICS
CHAPTER 1
Functions
1.3 Trigonometric Functions and Their Inverses
IDENTITIES, EQUATIONS, AND INEQUALITIES
There are a few trigonometric identities you must know for the Mathematics Level 2 Subject Test.
• Reciprocal Identities recognize the definitional relationships:
• Cofunction Identities were discussed earlier. Using radian measure:
• Pythagorean Identities 
• Double Angle Formulas 
EXAMPLES
1. Given cos 
and 
, find 
Since sin 2
= 2(sin )(cos ), you need to determine the value of sin . From the figure below, you can see that sin 
. Therefore, sin 
.
2. If cos 23° = z, find the value of cos 46° in terms of z.
Since 46 = 2(23), a double angle formula can be used: cos 2A = 2 cos2 A – 1. Substituting 23° for A, cos 46° = cos 2(23°) = 2 cos2 23° – 1 = 2(cos 23°)2 – 1 = 2z 2 – 1.
3. If sin x = A, find cos 2x in terms of A.
Using the identity cos 2x = 1 – sin2 x, you get cos 2x = 1 – A2.
You may be expected to solve trigonometric equations on the Math Level 2 Subject Test by using your graphing calculator and getting answers that are decimal approximations. To solve any equation, enter each side of the equation into a function (Yn), graph both functions, and find the point(s) of intersection on the indicated domain by choosing an appropriate window.
4. Solve 2 sin x + cos 2x = 2 sin2 x – 1 for 0 
x 2
.
Enter 2 sin x + cos 2x into Y1 and 2 sin2 x – 1 into Y2. Set Xmin = 0, Xmax = 2, Ymin = –4, and Ymax = 4. Solutions (x-coordinates of intersection points) are 1.57, 3.67, and 5.76.
5. Find values of x on the interval [0,] for which cos x < sin 2x.
Enter each side of the inequality into a function, graph both, and find the values of x where the graph of cos x lies beneath the graph of sin 2x: 0.52 < x < 1.57 or x > 2.62.
EXERCISES
1. If sin 
and cos 
, find the value of sin 2x.
(A) –
(B) –
(C)
(D)
(E) 
2. If tan A = cot B, then
(A) A = B
(B) A = 90° + B
(C) B = 90° + A
(D) A + B = 90°
(E) A + B = 180°
3. If cos 
, find cos 2x.
(A) –0.87
(B) –0.25
(C) 0
(D) 0.5
(E) 0.75
4. If sin 37° = z, express sin 74° in terms of z.
(A) 
(B) 2z 2 + 1
(C) 2z
(D) 2z 2 – 1
(E) 
5. If sin x = –0.6427, what is csc x?
(A) –1.64
(B) –1.56
(C) 0.64
(D) 1.56
(E) 1.70
6. For what value(s) of x, 0 < x < 
, is sin x < cos x?
(A) x < 0.79
(B) x < 0.52
(C) 0.52 < x < 0.79
(D) x > 0.52
(E) x > 0.79
7. What is the range of the function f(x) = 5 – 6sin (x + 1)?
(A) [–6,6]
(B) [–5,5]
(C) [–1,1]
(D) [–1,11]
(E) [–11,1]