Question 1

Evaluate the following expression. ​
(1 + sin 5y)(1 + sin (- 5y))
​

Accepted Answer

A) sin25y 
B) cos22y 
C) - sin25y 
D) - cos25y 
E) cos25y 
A) sin25y 
B) cos22y 
C) - sin25y 
D) - cos25y 
E) cos25y

Question 2

Which of the following expressions is equivalent to $$\frac { 5 \cot ^ { 2 } t } { \csc t }$$ ? (t ? ?n,where n is a whole number) ?

Accepted Answer

A) ? $\frac { 5 - 5 \sin ^ { 2 } t } { \sin t }$ 
B)  $\frac { - 1 - \sin ^ { 2 } t } { 5 \sin t }$ 
C)  $\frac { 5 - 5 \cos ^ { 2 } t } { \cos t }$ 
D)  $\frac { 5 + 5 \sin ^ { 2 } t } { \sin t }$ 
E)  $\frac { 5 + 5 \cos ^ { 2 } t } { \cos t }$ 
A) ? $\frac { 5 - 5 \sin ^ { 2 } t } { \sin t }$ 
B)  $\frac { - 1 - \sin ^ { 2 } t } { 5 \sin t }$ 
C)  $\frac { 5 - 5 \cos ^ { 2 } t } { \cos t }$ 
D)  $\frac { 5 + 5 \sin ^ { 2 } t } { \sin t }$ 
E)  $\frac { 5 + 5 \cos ^ { 2 } t } { \cos t }$

Question 3

Evaluate the following expression.(x ? ?/10 + ?n,where n is a whole number)? $5 \cos 5 x - \frac { 5 \cos 5 x } { 1 - \tan 5 x }$ ?

Accepted Answer

A)  $\frac { 10 \sin 5 x \cos 5 x } { \sin 5 x - \cos 5 x }$ 
B)  $\frac { - 5 \sin 5 x \cos 5 x } { \sin 5 x + \cos 5 x }$ 
C)  $\frac { 5 \sin 5 x \cos 5 x } { \sin 5 x - \cos 5 x }$ 
D)  $\frac { - 5 \sin 5 x \cos 5 x } { \sin 5 x - \cos 5 x }$ 
E)  $\frac { 5 \sin 5 x \cos 5 x } { \sin 5 x + \cos 5 x }$ 
A)  $\frac { 10 \sin 5 x \cos 5 x } { \sin 5 x - \cos 5 x }$ 
B)  $\frac { - 5 \sin 5 x \cos 5 x } { \sin 5 x + \cos 5 x }$ 
C)  $\frac { 5 \sin 5 x \cos 5 x } { \sin 5 x - \cos 5 x }$ 
D)  $\frac { - 5 \sin 5 x \cos 5 x } { \sin 5 x - \cos 5 x }$ 
E)  $\frac { 5 \sin 5 x \cos 5 x } { \sin 5 x + \cos 5 x }$

Question 4

Which of the following expressions is equivalent to $$\frac { 2 \cot ^ { 3 } t } { \csc t }$$ ? (a ? ?n,where n is a whole number) ?

Accepted Answer

A) sin t (2 - 2 csc2t) 
B) cos t (2 csc2t - 2) 
C) cos t (2 - 2 csc2t) 
D) sin t (2 csc2t - 2) 
E) tan t (2 csc2t - 2) 
A) sin t (2 - 2 csc2t) 
B) cos t (2 csc2t - 2) 
C) cos t (2 - 2 csc2t) 
D) sin t (2 csc2t - 2) 
E) tan t (2 csc2t - 2)

Question 5

Evaluate the following expression.(? ? ?n,where n is a whole number)? $\frac { 5 \cos 4 \theta \cot 4 \theta } { 1 - \sin 4 \theta } - 5$ ?

Accepted Answer

A) 5 sec 4? 
B) - 5 csc 4? 
C) 5 csc 4? 
D) - 5 sec 4? 
E) 5 cot 4? 
A) 5 sec 4? 
B) - 5 csc 4? 
C) 5 csc 4? 
D) - 5 sec 4? 
E) 5 cot 4?

Question 6

Evaluate the expression.? $$\frac { 1 } { \tan x + \cot x }$$ ?

Accepted Answer

A)  $- \sin ^ { 2 } x$ 
B)  $\sin x$ 
C)  $\sin x \cos x$ 
D)  $\cos ^ { 2 } x$ 
E) 0 
A)  $- \sin ^ { 2 } x$ 
B)  $\sin x$ 
C)  $\sin x \cos x$ 
D)  $\cos ^ { 2 } x$ 
E) 0

Question 7

Evaluate the following expression.(t ? ?/2+?n,where n is a whole number)? $$2 \sin t \csc \left( \frac { \pi } { 2 } - t \right)$$ ?

Accepted Answer

A) - 2 tan t 
B) 2 tan t 
C) 2 sin t 
D) - 2 cot t 
E) 2 cot t 
A) - 2 tan t 
B) 2 tan t 
C) 2 sin t 
D) - 2 cot t 
E) 2 cot t

Question 8

Which of the following expressions is equivalent to $\frac { \cot 3 x } { \sec 3 x }$ ? (x ? (?/3)n,where n is a whole number) ?

Accepted Answer

A) -3 sec x - sin x 
B) csc 3x - sin 3x 
C) csc 3x + sin 3x 
D) -3 csc x + sin x 
E) - csc x -3 sin x 
A) -3 sec x - sin x 
B) csc 3x - sin 3x 
C) csc 3x + sin 3x 
D) -3 csc x + sin x 
E) - csc x -3 sin x

Question 9

Evaluate the following expression.(x ≠ π/2+πn,where n is a whole number) ​
Tan7x sec2x - tan7x
​

Accepted Answer

A) 9 tan9x 
B) tan2x 
C) tan9x 
D) 7 tan7x 
E) tan7x 
A) 9 tan9x 
B) tan2x 
C) tan9x 
D) 7 tan7x 
E) tan7x

Question 10

Evaluate the following expression.(x ? ?n,where n is a whole number)? $\frac { 3 } { \sin x } - \frac { 3 } { \csc x }$ ?

Accepted Answer

A) 3 (csc x - sin x) 
B) (csc x + sin x) 
C) - 3 (csc x - sin x) 
D) 3 (csc x + sin x) 
E) (csc x - sin x) 
A) 3 (csc x - sin x) 
B) (csc x + sin x) 
C) - 3 (csc x - sin x) 
D) 3 (csc x + sin x) 
E) (csc x - sin x)

Question 11

Evaluate the following expression.(a ? ?/2+?n,where n is a whole number)? $$\frac { 5 \tan ^ { 2 } \theta } { \sec \theta }$$ ?

Accepted Answer

A) 5 cos ? tan ? 
B) 5 tan ? sec ? 
C) 5 sin ? tan ? 
D) 5 cos ? cot ? 
E) 5 cot ? sec ? 
A) 5 cos ? tan ? 
B) 5 tan ? sec ? 
C) 5 sin ? tan ? 
D) 5 cos ? cot ? 
E) 5 cot ? sec ?

Question 12

Evaluate the following expression. ​
Cot2t (2 sec2t - 2)
​

Accepted Answer

A) 2 
B) 0 
C) 3 
D) 4 
E) 1 
A) 2 
B) 0 
C) 3 
D) 4 
E) 1

Question 13

Evaluate the following expression.(x ≠ π/2+πn,where n is a whole number) ​
Sec5x (sec x tan x)- ​sec3x (sec x tan x)
​

Accepted Answer

A) ​sec4x tan x 
B) ​4 sec x tan4 x 
C) ​sec3x tan5x 
D) ​sec4x tan3 x 
E) ​sec3x tan3x 
A) ​sec4x tan x 
B) ​4 sec x tan4 x 
C) ​sec3x tan5x 
D) ​sec4x tan3 x 
E) ​sec3x tan3x

Question 14

Evaluate the following expression. ​
4 sec y cos y
​

Accepted Answer

A) 5 
B) 3 
C) 6 
D) 7 
E) 4 
A) 5 
B) 3 
C) 6 
D) 7 
E) 4

Question 15

Evaluate the following expression.(x ≠ π/2+πn,where n is a whole number) ​
2 cos x + 2 sin x tan x
​

Accepted Answer

A) -2 sec x 
B) 2 sec x 
C) 4 cos x 
D) -4 cos x 
E) 3 sin x 
A) -2 sec x 
B) 2 sec x 
C) 4 cos x 
D) -4 cos x 
E) 3 sin x

Question 16

Use the cofunction identities to evaluate the expression below without using calculator. sin220° + sin227° + sin270° + sin263°

Accepted Answer

A) 1 
B)  $\frac { 1 } { 2 }$ 
C) -1 
D) ?0 
E) 2 
A) 1 
B)  $\frac { 1 } { 2 }$ 
C) -1 
D) ?0 
E) 2

Question 17

Evaluate the following expression. ​
(sin2x - sin4x)cos x
​

Accepted Answer

A) cos4x sin2x 
B) cos2x sin2x 
C) cos2x sin6x 
D) cos3x sin2x 
E) cos x sin x 
A) cos4x sin2x 
B) cos2x sin2x 
C) cos2x sin6x 
D) cos3x sin2x 
E) cos x sin x

Question 18

Evaluate the following expression.(x ? ?n,y ? ?/12 + ?n,where n is a whole number)? $\frac { 7 \tan 6 x + 7 \cot 6 y } { \tan 6 x \cot 6 y }$ ?

Accepted Answer

A) 7 tan 6x + 7 cot 6y 
B) 7 tan 6y - 7 cot 6x 
C) 7 tan 6y + 7 cot 6x 
D) - (7 tan 6y + 7 cot 6x) 
E) 7 tan 6x - 7 cot 6y 
A) 7 tan 6x + 7 cot 6y 
B) 7 tan 6y - 7 cot 6x 
C) 7 tan 6y + 7 cot 6x 
D) - (7 tan 6y + 7 cot 6x) 
E) 7 tan 6x - 7 cot 6y

Question 19

Evaluate the following expression.(x ≠ (π + 2πn)/10,where n is a whole number) ​
Sec 5x - cos 5x
​

Accepted Answer

A) - 5 sin 5x cot 5x 
B) - sin 5x tan 5x 
C) sin 5x csc 5x 
D) 5 sin 5x cot x 
E) sin 5x tan 5x 
A) - 5 sin 5x cot 5x 
B) - sin 5x tan 5x 
C) sin 5x csc 5x 
D) 5 sin 5x cot x 
E) sin 5x tan 5x

Question 20

Evaluate the following expression.(x ? ?/2 + ?n,where n is a whole number)? $\frac { 11 \cos \left[ \frac { \pi } { 2 } - x \right] } { \sin \left[ \frac { \pi } { 2 } - x \right] }$ ?

Accepted Answer

A) - 11 tan x 
B) 11 cot x 
C) 12 tan x 
D) - 11 cot x 
E) 11 tan x 
A) - 11 tan x 
B) 11 cot x 
C) 12 tan x 
D) - 11 cot x 
E) 11 tan x

Exam 32: Verifying Trigonometric Equations

Evaluate the following expression. ​ (1 + sin 5y)(1 + sin (- 5y)) ​

Which of the following expressions is equivalent to 5cot⁡2tcsc⁡t\frac { 5 \cot ^ { 2 } t } { \csc t }csct5cot2t​ ? (t ? ?n,where n is a whole number) ?

Evaluate the following expression.(x ? ?/10 + ?n,where n is a whole number)? 5cos⁡5x−5cos⁡5x1−tan⁡5x5 \cos 5 x - \frac { 5 \cos 5 x } { 1 - \tan 5 x }5cos5x−1−tan5x5cos5x​ ?

Which of the following expressions is equivalent to 2cot⁡3tcsc⁡t\frac { 2 \cot ^ { 3 } t } { \csc t }csct2cot3t​ ? (a ? ?n,where n is a whole number) ?

Evaluate the following expression.(? ? ?n,where n is a whole number)? 5cos⁡4θcot⁡4θ1−sin⁡4θ−5\frac { 5 \cos 4 \theta \cot 4 \theta } { 1 - \sin 4 \theta } - 51−sin4θ5cos4θcot4θ​−5 ?

Evaluate the expression.? 1tan⁡x+cot⁡x\frac { 1 } { \tan x + \cot x }tanx+cotx1​ ?

Evaluate the following expression.(t ? ?/2+?n,where n is a whole number)? 2sin⁡tcsc⁡(π2−t)2 \sin t \csc \left( \frac { \pi } { 2 } - t \right)2sintcsc(2π​−t) ?

Which of the following expressions is equivalent to cot⁡3xsec⁡3x\frac { \cot 3 x } { \sec 3 x }sec3xcot3x​ ? (x ? (?/3)n,where n is a whole number) ?

Evaluate the following expression.(x ≠ π/2+πn,where n is a whole number) ​ Tan7x sec2x - tan7x ​

Evaluate the following expression.(x ? ?n,where n is a whole number)? 3sin⁡x−3csc⁡x\frac { 3 } { \sin x } - \frac { 3 } { \csc x }sinx3​−cscx3​ ?

Evaluate the following expression.(a ? ?/2+?n,where n is a whole number)? 5tan⁡2θsec⁡θ\frac { 5 \tan ^ { 2 } \theta } { \sec \theta }secθ5tan2θ​ ?

Evaluate the following expression. ​ Cot2t (2 sec2t - 2) ​

Evaluate the following expression.(x ≠ π/2+πn,where n is a whole number) ​ Sec5x (sec x tan x)- ​sec3x (sec x tan x) ​

Evaluate the following expression. ​ 4 sec y cos y ​

Evaluate the following expression.(x ≠ π/2+πn,where n is a whole number) ​ 2 cos x + 2 sin x tan x ​

Use the cofunction identities to evaluate the expression below without using calculator. sin220° + sin227° + sin270° + sin263°

Evaluate the following expression. ​ (sin2x - sin4x)cos x ​

Evaluate the following expression.(x ? ?n,y ? ?/12 + ?n,where n is a whole number)? 7tan⁡6x+7cot⁡6ytan⁡6xcot⁡6y\frac { 7 \tan 6 x + 7 \cot 6 y } { \tan 6 x \cot 6 y }tan6xcot6y7tan6x+7cot6y​ ?

Evaluate the following expression.(x ≠ (π + 2πn)/10,where n is a whole number) ​ Sec 5x - cos 5x ​

Evaluate the following expression.(x ? ?/2 + ?n,where n is a whole number)? 11cos⁡[π2−x]sin⁡[π2−x]\frac { 11 \cos \left[ \frac { \pi } { 2 } - x \right] } { \sin \left[ \frac { \pi } { 2 } - x \right] }sin[2π​−x]11cos[2π​−x]​ ?

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Evaluate the following expression. (1 + sin 5y)(1 + sin (- 5y))

Which of the following expressions is equivalent to $\frac { 5 \cot ^ { 2 } t } { \csc t }$ ? (t ? ?n,where n is a whole number) ?

Evaluate the following expression.(x ? ?/10 + ?n,where n is a whole number)? $5 \cos 5 x - \frac { 5 \cos 5 x } { 1 - \tan 5 x }$ ?

Which of the following expressions is equivalent to $\frac { 2 \cot ^ { 3 } t } { \csc t }$ ? (a ? ?n,where n is a whole number) ?

Evaluate the following expression.(? ? ?n,where n is a whole number)? $\frac { 5 \cos 4 \theta \cot 4 \theta } { 1 - \sin 4 \theta } - 5$ ?

Evaluate the expression.? $\frac { 1 } { \tan x + \cot x }$ ?

Evaluate the following expression.(t ? ?/2+?n,where n is a whole number)? $2 \sin t \csc \left( \frac { \pi } { 2 } - t \right)$ ?

Which of the following expressions is equivalent to $\frac { \cot 3 x } { \sec 3 x }$ ? (x ? (?/3)n,where n is a whole number) ?

Evaluate the following expression.(x ≠ π/2+πn,where n is a whole number) Tan⁷x sec²x - tan⁷x

Evaluate the following expression.(x ? ?n,where n is a whole number)? $\frac { 3 } { \sin x } - \frac { 3 } { \csc x }$ ?

Evaluate the following expression.(a ? ?/2+?n,where n is a whole number)? $\frac { 5 \tan ^ { 2 } \theta } { \sec \theta }$ ?

Evaluate the following expression. Cot²t (2 sec²t - 2)

Evaluate the following expression.(x ≠ π/2+πn,where n is a whole number) Sec⁵x (sec x tan x)- sec³x (sec x tan x)

Evaluate the following expression. 4 sec y cos y

Evaluate the following expression.(x ≠ π/2+πn,where n is a whole number) 2 cos x + 2 sin x tan x

Use the cofunction identities to evaluate the expression below without using calculator. sin²20° + sin²27° + sin²70° + sin²63°

Evaluate the following expression. (sin²x - sin⁴x)cos x

Evaluate the following expression.(x ? ?n,y ? ?/12 + ?n,where n is a whole number)? $\frac { 7 \tan 6 x + 7 \cot 6 y } { \tan 6 x \cot 6 y }$ ?

Evaluate the following expression.(x ≠ (π + 2πn)/10,where n is a whole number) Sec 5x - cos 5x

Evaluate the following expression.(x ? ?/2 + ?n,where n is a whole number)? $\frac { 11 \cos \left[ \frac { \pi } { 2 } - x \right] } { \sin \left[ \frac { \pi } { 2 } - x \right] }$ ?