Chapter Review of Trig Identities and Equations
Chapter
Chapter 7
Section
Chapter Review of Trig Identities and Equations
Solutions 33 Videos

Which trigonometric ratio is equivalent to the trigonometric ratio below.

 \displaystyle \sin \frac{3\pi}{10} 

0.48mins
Q1a

Which trigonometric ratio is equivalent to the trigonometric ratio below.

 \displaystyle \cos \frac{6\pi}{7} 

0.46mins
Q1b

Which trigonometric ratio is equivalent to the trigonometric ratio below.

 \displaystyle -\sin \frac{13\pi}{7} 

0.36mins
Q1c

Which trigonometric ratio is equivalent to the trigonometric ratio below.

 \displaystyle -\cos \frac{8\pi}{7} 

0.33mins
Q1d

Write an equation that is equivalent to

 \displaystyle y = -5\sin(x -\frac{\pi}{2}) - 8  , using the cosine function.

0.51mins
Q2

Use a compound angle formula to determine a trigonometric expression that is equivalent to the expressions.

 \displaystyle \sin(x - \frac{4\pi}{3}) 

1.09mins
Q3a

Use a compound angle formula to determine a trigonometric expression that is equivalent to the expressions.

 \displaystyle \cos(x + \frac{3\pi}{4}) 

1.01mins
Q3b

Use a compound angle formula to determine a trigonometric expression that is equivalent to the expressions.

 \displaystyle \tan (x + \frac{\pi}{3}) 

0.24mins
Q3c

Use a compound angle formula to determine a trigonometric expression that is equivalent to the expressions.

 \displaystyle \cos(x - \frac{5\pi}{4}) 

0.50mins
Q3d

Evaluate the expression.

 \displaystyle \frac{\tan \frac{\pi}{12} + \tan\frac{7\pi}{4}}{1 -\tan\frac{\pi}{12}\tan\frac{7\pi}{4}} 

1.07mins
Q4a

Evaluate the expression.

 \displaystyle \cos \frac{\pi}{9} \cos\frac{19\pi}{18} - \sin \frac{\pi}{9}\sin \frac{19\pi}{18} 

0.54mins
Q4b

Simplify the expression.

 \displaystyle 2\sin \frac{\pi}{12}\cos\frac{\pi}{12} 

0.18mins
Q5a

Simplify the expression.

 \displaystyle \cos^2 \frac{\pi}{12} - \sin^2 \frac{\pi}{12} 

0.19mins
Q5b

Simplify the expression.

 \displaystyle 1 - 2\sin^2\frac{3\pi}{8} 

0.39mins
Q5c

Simplify the expression.

 \displaystyle \frac{2\tan \frac{\pi}{6}}{1 - \tan^2\frac{\pi}{6}} 

0.26mins
Q5d

Determine the values of \sin 2x, \cos 2x, and \tan 2x, given

\sin x =\dfrac{3}{5}, and x is acute.

2.00mins
Q6a

Determine the values of \sin 2x, \cos 2x, and \tan 2x, given

\cot x = - \dfrac{7}{24}, and x is obtuse.

2.25mins
Q6b

Determine the values of \sin 2x, \cos 2x, and \tan 2x, given

\cos x =\dfrac{12}{13}, and \frac{3\pi}{2} \leq x \leq 2\pi

1.58mins
Q6c

Determine whether each of the following is a trigonometric equation or a trigonometric identity.

 \displaystyle \tan 2x = \frac{2\sin x\cos x}{1 -2\sin^2x} 

1.27mins
Q7a

Determine whether each of the following is a trigonometric equation or a trigonometric identity.

 \displaystyle \sec^2 x - \tan^2x = \cos x 

0.36mins
Q7b

Determine whether each of the following is a trigonometric equation or a trigonometric identity.

 \displaystyle \csc^2x -\cot^2x = \sin^2x + \cos^2x 

0.26mins
Q7c

Determine whether each of the following is a trigonometric equation or a trigonometric identity.

 \displaystyle \tan^2x = 1 

0.25mins
Q7d

Prove that  \displaystyle \frac{1 - \sin^2x}{\cot^2x} = 1 -\cos^2x  is a trigonometric identity.

1.19mins
Q8

Prove that  \displaystyle \frac{2\sec^2x -2\tan^2 x}{\csc x} = \sin 2x\sec x  is a trigonometric identity.

1.48mins
Q9

Solve for when 0 \leq x \leq 2\pi

\frac{2}{\sin x} + 10 = 6

0.44mins
Q10a

Solve for when 0 \leq x \leq 2\pi

 \displaystyle -\frac{5\cot x}{2} + \frac{7}{3} = - \frac{1}{6} 

1.07mins
Q10b

Solve for when 0 \leq x \leq 2\pi

 \displaystyle 3 + 10 \sec x - 1 = -18 

0.48mins
Q10c

a) Solve the equation y^2 - 4 = 0.

b) Solve \csc^2x - 4 = 0 in the interval 0 \leq x \leq 2\pi

1.09mins
Q11

Solve the equation for x in the interval 0 \leq x \leq 2\pi

 \displaystyle 2\sin^2 x - \sin x - 1 =0 

0.46mins
Q12a

Solve the equation for x in the interval 0 \leq x \leq 2\pi

 \displaystyle \tan^2x \sin x - \frac{\sin x}{3} = 0 

1.01mins
Q12b

Solve the equation for x in the interval 0 \leq x \leq 2\pi

 \displaystyle \cos^2x + (\frac{1- \sqrt{2}}{2})\cos x - \frac{\sqrt{2}}{4} = 0 

1.32mins
Q12c

Solve the equation for x in the interval 0 \leq x \leq 2\pi

 \displaystyle 25 \tan^2x - 70\tan x = -49 

Solve the equation \dfrac{1}{1 +\tan^2x} = -\cos x for x in the interval 0 \leq x \leq 2\pi