Question 1

Show that the equation is not an identity by finding a value of x for which both sides are defined but not equal.
-$\cos ( x + \pi ) = \cos x$

Accepted Answer

A)  0 
B)  $\frac { \pi } { 2 }$ 
C)  $- \frac { \pi } { 2 }$ 
D)  $\frac { 3 \pi } { 2 }$ 
A)  0 
B)  $\frac { \pi } { 2 }$ 
C)  $- \frac { \pi } { 2 }$ 
D)  $\frac { 3 \pi } { 2 }$

Question 2

Use substitution to determine whether the given x-value is a solution of the equation.
Find All Solutions of a Trigonometric Equation
-$2 \cos x - 1 = 0$

Accepted Answer

A)  $x = \frac { \pi } { 3 } + 2 n \pi$ or $x = \frac { 5 \pi } { 3 } + 2 n \pi$ 
B)  $x = \frac { \pi } { 3 } + n \pi$ or $x = \frac { 5 \pi } { 3 } + n \pi$ 
C)  $x = \frac { 4 \pi } { 3 } + 2 n \pi$ or $x = \frac { 5 \pi } { 6 } + 2 n \pi$ 
D)  $x = \frac { 4 \pi } { 3 } + n \pi$ or $x = \frac { 5 \pi } { 6 } + n \pi$ 
A)  $x = \frac { \pi } { 3 } + 2 n \pi$ or $x = \frac { 5 \pi } { 3 } + 2 n \pi$ 
B)  $x = \frac { \pi } { 3 } + n \pi$ or $x = \frac { 5 \pi } { 3 } + n \pi$ 
C)  $x = \frac { 4 \pi } { 3 } + 2 n \pi$ or $x = \frac { 5 \pi } { 6 } + 2 n \pi$ 
D)  $x = \frac { 4 \pi } { 3 } + n \pi$ or $x = \frac { 5 \pi } { 6 } + n \pi$

Question 3

Express the product as a sum or difference.
-$\sin 7 x \cos 4 x$

Accepted Answer

A)  $\frac { 1 } { 2 } ( \sin 11 x + \sin 3 x )$ 
B)  $\sin \left( \cos 28 x ^ { 2 } \right)$ 
C)  $\frac { 1 } { 2 } ( \cos 11 x - \cos 3 x )$ 
D)  $\frac { 1 } { 2 } ( \sin 11 x + \cos 3 x )$ 
A)  $\frac { 1 } { 2 } ( \sin 11 x + \sin 3 x )$ 
B)  $\sin \left( \cos 28 x ^ { 2 } \right)$ 
C)  $\frac { 1 } { 2 } ( \cos 11 x - \cos 3 x )$ 
D)  $\frac { 1 } { 2 } ( \sin 11 x + \cos 3 x )$

Question 4

Find the exact value under the given conditions.
-$\sin \alpha = \frac { 21 } { 29 } , 0 < \alpha < \frac { \pi } { 2 } ; \quad \cos \beta = \frac { 7 } { 25 } , 0 < \beta < \frac { \pi } { 2 } \quad$ Find $\tan ( \alpha + \beta )$.

Accepted Answer

A)  $- \frac { 627 } { 364 }$ 
B)  $\frac { 644 } { 725 }$ 
C)  $- \frac { 364 } { 725 }$ 
D)  $\frac { 627 } { 725 }$ 
A)  $- \frac { 627 } { 364 }$ 
B)  $\frac { 644 } { 725 }$ 
C)  $- \frac { 364 } { 725 }$ 
D)  $\frac { 627 } { 725 }$

Question 5

Use Sum and Difference Formulas for Tangents
Find the exact value by using a difference identity.
-$$\frac { \tan 70 ^ { \circ } - \tan \left( - 50 ^ { \circ } \right) } { 1 + \tan 70 ^ { \circ } \tan \left( - 50 ^ { \circ } \right) }$$

Accepted Answer

A)  $- \sqrt { 3 }$ 
B)  $- \frac { \sqrt { 3 } } { 3 }$ 
C)  $- \frac { 1 } { 2 }$ 
D)  $- 2$ . 
A)  $- \sqrt { 3 }$ 
B)  $- \frac { \sqrt { 3 } } { 3 }$ 
C)  $- \frac { 1 } { 2 }$ 
D)  $- 2$ .

Question 6

Use substitution to determine whether the given x-value is a solution of the equation.
Find All Solutions of a Trigonometric Equation
-$$\sin x = - \frac { \sqrt { 3 } } { 2 } , \quad x = \frac { - 2 \pi } { 3 }$$

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Show that the equation is not an identity by finding a value of x for which both sides are defined but not equal. - $\cos ( x + \pi ) = \cos x$

Use substitution to determine whether the given x-value is a solution of the equation. Find All Solutions of a Trigonometric Equation - $2 \cos x - 1 = 0$

Express the product as a sum or difference. - $\sin 7 x \cos 4 x$

Find the exact value under the given conditions. - $\sin \alpha = \frac { 21 } { 29 } , 0 < \alpha < \frac { \pi } { 2 } ; \quad \cos \beta = \frac { 7 } { 25 } , 0 < \beta < \frac { \pi } { 2 } \quad$ Find $\tan ( \alpha + \beta )$ .

Use Sum and Difference Formulas for Tangents Find the exact value by using a difference identity. - $\frac { \tan 70 ^ { \circ } - \tan \left( - 50 ^ { \circ } \right) } { 1 + \tan 70 ^ { \circ } \tan \left( - 50 ^ { \circ } \right) }$

Use substitution to determine whether the given x-value is a solution of the equation. Find All Solutions of a Trigonometric Equation - $\sin x = - \frac { \sqrt { 3 } } { 2 } , \quad x = \frac { - 2 \pi } { 3 }$

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Additional Topics in Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections and Analytic Geometry

Sequences, Induction, and Probability

Prerequisites: Fundamental Concepts of Algebra

Filters

Exam 6: Analytic Trigonometry

Show that the equation is not an identity by finding a value of x for which both sides are defined but not equal. - cos⁡(x+π)=cos⁡x\cos ( x + \pi ) = \cos xcos(x+π)=cosx

Use substitution to determine whether the given x-value is a solution of the equation. Find All Solutions of a Trigonometric Equation - 2cos⁡x−1=02 \cos x - 1 = 02cosx−1=0

Express the product as a sum or difference. - sin⁡7xcos⁡4x\sin 7 x \cos 4 xsin7xcos4x

Use substitution to determine whether the given x-value is a solution of the equation. Find All Solutions of a Trigonometric Equation - sin⁡x=−32,x=−2π3\sin x = - \frac { \sqrt { 3 } } { 2 } , \quad x = \frac { - 2 \pi } { 3 }sinx=−23​​,x=3−2π​