Download Practice for Test 2

Practice for Test 2
A) Find the exact value of the expression
a.
b.
c.
d.
e.
f.
B) Find the inverse function f-1 of the function f
a. f(x) =2 sin x – 5
b. f(x) =7 tan 8x
c. f(x) = cos(x-6) – 7
C) Find the domain of f and f-1
a. f(x) = -5cos(9x)
b. f(x) = 5sin(8x-1)
c. f(x) = tan(x-3) + 6
D) Find the exact solution of the equation
𝜋
a. –sin-1(4x) =
4
b. 2 cos-1x = 𝜋
c. -4 tan-1 x = 𝜋
E)
F) Write the trigonometric expression as an algebraic expression in u:
a. sin (cot-1u)
b. cos (csc-1u)
c. tan (sec-1u)
G) Simplify the following expressions using the directions provided:
H) Simplify the expression:
a.
b.
G) Establish the following identities
H) Complete the follwing identities (multiple choice).
1.
2.
3.
4.
5.
6.
I)
Use sum and difference formulas to fin exact values of the following expressions:
a. cos 285°
5𝜋
b. tan
c.
d.
12
11𝜋
sin−
12
1−tan 80°tan70°
tan 80°−tan70°
J) Find the exact values under the specified conditions
a.
b.
c.
K) Establish the following identities using sum and difference formulae.
L) Complete the following identities using sum and difference formulae.
M) Write the trigonometric expressions as algebraic expressions containing u and v.
1.
2.
3.
N) Solve the following trig equations on the interval 0 ≤θ<2𝜋
1. 𝑠𝑖𝑛𝜃 + 𝑐𝑜𝑠𝜃 = 0
2. 𝑠𝑖𝑛𝜃 = 𝑐𝑜𝑠𝜃
3. √3𝑠𝑖𝑛𝜃 − 𝑐𝑜𝑠𝜃 = −1
O) Use the information given about the angle to 𝜃, 0 ≤ 𝜃 ≤ 2𝜋, to find the exact value of the
indicated trigonometric functions.
7
𝜋
1. 𝑠𝑖𝑛𝜃 = , 0 < 𝜃 < , find cos 2θ.
25
20
2. 𝑡𝑎𝑛𝜃 =
21
2
3𝜋
,𝜋 < 𝜃 <
2
, find sin 2θ.
P) Solve the problem
4
1. If sin θ = − , and θ terminates in Quadrant IV, then find sin 2θ.
5
7
2. If tan θ = − , and θ terminates in Quadrant III, then find cos 2θ.
24
Q)
R) Use the information given about the angle to 𝜃, 0 ≤ 𝜃 ≤ 2𝜋, to find the exact value of the
indicated trigonometric functions (use half angle formulae).
1
𝜋
4
2
θ
1. 𝑠𝑖𝑛𝜃 = , 0 < 𝜃 < , find sin .
2. 𝑡𝑎𝑛𝜃 = 3 , 𝜋 ≤ 𝜃 ≤
3𝜋
2
2
θ
, find tan .
2
S) The polar coordinates of a point are given. Find the rectangular coordinates of the point.
a.
b. (-3, -135 °)
c. (-3, 45°)
T) The rectangular coordinates of a point are given. Find polar coordinates for the point.
a. (8, 0)
b. (√3, −1)
U) The letters x and y represent rectangular coordinates. Write the equation using polar
coordinates (r, θ).
a. x2 + y2 - 4x = 0
b. x2 + 4y2 = 4
c. xy = 1
d. y = 5
V) The letters r and θ represent polar coordinates. Write the equation using rectangular
coordinates (x, y).
a.
b.