Filters
Question type
Study Flashcards

Verify the identity shown below. 1sec⁡θ−tan⁡θ=sec⁡θ+tan⁡θ\frac { 1 } { \sec \theta - \tan \theta } = \sec \theta + \tan \theta

Correct Answer

verifed

verified

None...

View Answer

Determine which of the following are trigonometric identities. I. sin⁡(y) −sin⁡(x) cos⁡(y) +cos⁡(x) +cos⁡(y) −cos⁡(x) sin⁡(y) +sin⁡(x) =0\frac { \sin ( y ) - \sin ( x ) } { \cos ( y ) + \cos ( x ) } + \frac { \cos ( y ) - \cos ( x ) } { \sin ( y ) + \sin ( x ) } = 0 II. sin⁡(y) +sin⁡(x) cos⁡(y) +cos⁡(x) +cos⁡(y) +cos⁡(x) sin⁡(y) +sin⁡(x) =1\frac { \sin ( y ) + \sin ( x ) } { \cos ( y ) + \cos ( x ) } + \frac { \cos ( y ) + \cos ( x ) } { \sin ( y ) + \sin ( x ) } = 1 III. sin⁡(y) +cos⁡(x) sin⁡(y) cos⁡(x) =sin⁡(x) +cos⁡(y) \frac { \sin ( y ) + \cos ( x ) } { \sin ( y ) \cos ( x ) } = \sin ( x ) + \cos ( y )


A) I is the only identity.
B) II and II are the only identities.
C) I, II, and III are identities.
D) I and III are the only identities.
E) II is the only identity.

Correct Answer

verifed

verified

Determine which of the following are trigonometric identities. I. sin⁡(θ) +cot⁡(θ) cos⁡(θ) =csc⁡(θ) \sin ( \theta ) + \cot ( \theta ) \cos ( \theta ) = \csc ( \theta ) II. cot⁡(θ) −sin⁡(θ) cos⁡(θ) =0\cot ( \theta ) - \sin ( \theta ) \cos ( \theta ) = 0 III. sin⁡(θ) +sin⁡(θ) cos⁡(θ) =csc⁡(θ) \sin ( \theta ) + \sin ( \theta ) \cos ( \theta ) = \csc ( \theta )


A) I is the only identity.
B) I and II are the only identities.
C) III is the only identity.
D) I, II, and III are identities.
E) II is the only identity.

Correct Answer

verifed

verified

Determine which of the following are trigonometric identities. I. sin⁡(t) +sin⁡(s) cos⁡(t) −cos⁡(s) +cos⁡(t) +cos⁡(s) sin⁡(t) −sin⁡(s) =0\frac { \sin ( t ) + \sin ( s ) } { \cos ( t ) - \cos ( s ) } + \frac { \cos ( t ) + \cos ( s ) } { \sin ( t ) - \sin ( s ) } = 0 II. sin⁡(t) +sin⁡(s) cos⁡(t) +cos⁡(s) +cos⁡(t) +cos⁡(s) sin⁡(t) +sin⁡(s) =1\frac { \sin ( \mathrm { t } ) + \sin ( \mathrm { s } ) } { \cos ( \mathrm { t } ) + \cos ( \mathrm { s } ) } + \frac { \cos ( \mathrm { t } ) + \cos ( \mathrm { s } ) } { \sin ( \mathrm { t } ) + \sin ( \mathrm { s } ) } = 1 III. sin⁡(t) +cos⁡(s) sin⁡(t) cos⁡(s) =sin⁡(s) +cos⁡(t) \frac { \sin ( \mathrm { t } ) + \cos ( \mathrm { s } ) } { \sin ( \mathrm { t } ) \cos ( \mathrm { s } ) } = \sin ( \mathrm { s } ) + \cos ( \mathrm { t } )


A) I is the only identity.
B) I and III are the only identities.
C) II and II are the only identities.
D) I and II are the only identities.
E) I, II, and III are identities.

Correct Answer

verifed

verified

If x=8cos⁡θx = 8 \cos \theta , use trigonometric substitution to write 64−x2\sqrt { 64 - x ^ { 2 } } as a trigonometric function of θ\theta , where 0<θ<π0 < \theta < \pi .


A) 8sec⁡θ8 \sec \theta
B) 8sin⁡θ8 \sin \theta
C) 8cot⁡θ8 \cot \theta
D) 8cos⁡θ8 \cos \theta
E) 8csc⁡θ8 \csc \theta

Correct Answer

verifed

verified

Use fundamental identities to simplify the expression below and then determine which of the following is not equivalent. sin⁡α(csc⁡α−sin⁡α) \sin \alpha ( \csc \alpha - \sin \alpha )


A) 1−sin⁡2α1 - \sin ^ { 2 } \alpha
B) csc⁡2α−1csc⁡2α\frac { \csc ^ { 2 } \alpha - 1 } { \csc ^ { 2 } \alpha }
C) csc⁡2α−sec⁡2α+tan⁡2αcsc⁡2α\frac { \csc ^ { 2 } \alpha - \sec ^ { 2 } \alpha + \tan ^ { 2 } \alpha } { \csc ^ { 2 } \alpha }
D) 1−cot⁡2α1 - \cot ^ { 2 } \alpha
E) cos⁡2α\cos ^ { 2 } \alpha

Correct Answer

verifed

verified

Use the figure below to find the exact value of the given trigonometric expression. cot⁡x2\cot \frac { x } { 2 } Use the figure below to find the exact value of the given trigonometric expression. \cot \frac { x } { 2 } A) \cot \frac { x } { 2 } = \frac { \sqrt { 2 } } { 10 } B) \cot \frac { x } { 2 } = \frac { 1 } { 7 } C) \cot \frac { x } { 2 } = 7 D) \cot \frac { x } { 2 } = \frac { 7 \sqrt { 2 } } { 10 } E) \cot \frac { x } { 2 } = \frac { 7 } { 12 }


A) cot⁡x2=210\cot \frac { x } { 2 } = \frac { \sqrt { 2 } } { 10 }
B) cot⁡x2=17\cot \frac { x } { 2 } = \frac { 1 } { 7 }
C) cot⁡x2=7\cot \frac { x } { 2 } = 7
D) cot⁡x2=7210\cot \frac { x } { 2 } = \frac { 7 \sqrt { 2 } } { 10 }
E) cot⁡x2=712\cot \frac { x } { 2 } = \frac { 7 } { 12 }

Correct Answer

verifed

verified

Verify the identity shown below. sec⁡2(π2−y)−1=cot⁡2y\sec ^ { 2 } \left( \frac { \pi } { 2 } - y \right) - 1 = \cot ^ { 2 } y

Correct Answer

verifed

verified

None...

View Answer

Which of the following is a solution to the given equation? sec⁡x−2=0\sec x - 2 = 0


A) x=7π6x = \frac { 7 \pi } { 6 }
B) x=π4x = \frac { \pi } { 4 }
C) x=5π6x = \frac { 5 \pi } { 6 }
D) x=5π3x = \frac { 5 \pi } { 3 }
E) x=7π4x = \frac { 7 \pi } { 4 }

Correct Answer

verifed

verified

Solve the multiple-angle equation in the interval [0,2π) [ 0,2 \pi ) . tan⁡2x=−1\tan 2 x = - 1


A) x=π4,3π4,5π4,7π4x = \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 }
B) x=π3,2π3,4π3,5π3x = \frac { \pi } { 3 } , \frac { 2 \pi } { 3 } , \frac { 4 \pi } { 3 } , \frac { 5 \pi } { 3 }
C) x=3π8,7π8,11π8,15π8x = \frac { 3 \pi } { 8 } , \frac { 7 \pi } { 8 } , \frac { 11 \pi } { 8 } , \frac { 15 \pi } { 8 }
D) x=π6,5π6,7π6,11π6x = \frac { \pi } { 6 } , \frac { 5 \pi } { 6 } , \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }
E) x=π6,5π6,7π6,11π6x = \frac { \pi } { 6 } , \frac { 5 \pi } { 6 } , \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 } .

Correct Answer

verifed

verified

Find the exact solutions of the given equation in the interval [0,2π) [ 0,2 \pi ) . sin⁡2x=sin⁡x\sin 2 x = \sin x


A) x=2π3,π,4π3x = \frac { 2 \pi } { 3 } , \pi , \frac { 4 \pi } { 3 }
B) x=0,π3,π,5π3x = 0 , \frac { \pi } { 3 } , \pi , \frac { 5 \pi } { 3 }
C) x=π2,7π6,11π6x = \frac { \pi } { 2 } , \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }
D) x=0,π3,2π3,π,4π3,5π3x = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 } , \pi , \frac { 4 \pi } { 3 } , \frac { 5 \pi } { 3 }
E) x=0x = 0

Correct Answer

verifed

verified

Solve the following equation. tan⁡2x+tan⁡x=0\tan ^ { 2 } x + \tan x = 0


A) x=π+2nπx = \pi + 2 n \pi and x=3π2+2nπx = \frac { 3 \pi } { 2 } + 2 n \pi , where nn is an:
B) x=nπx = n \pi and x=3π4+nπx = \frac { 3 \pi } { 4 } + n \pi , where nn is an integer
C) x=2π3+2nπx = \frac { 2 \pi } { 3 } + 2 n \pi and x=5π3+2nπx = \frac { 5 \pi } { 3 } + 2 n \pi , where nn is at
D) x=nπx = n \pi and x=π2+nπx = \frac { \pi } { 2 } + n \pi , where nn is an integer
E) x=nπx = n \pi and x=3π2+2nπx = \frac { 3 \pi } { 2 } + 2 n \pi , where nn is an integ!

Correct Answer

verifed

verified

Solve the multiple-angle equation in the interval [0,2π) [ 0,2 \pi ) . sec⁡2x=2\sec 2 x = 2


A) x=π8,7π8,9π8,15π8x = \frac { \pi } { 8 } , \frac { 7 \pi } { 8 } , \frac { 9 \pi } { 8 } , \frac { 15 \pi } { 8 }
B) x=π12,5π12,13π12,17π12x = \frac { \pi } { 12 } , \frac { 5 \pi } { 12 } , \frac { 13 \pi } { 12 } , \frac { 17 \pi } { 12 }
C) x=π6,5π6,7π6,11π6x = \frac { \pi } { 6 } , \frac { 5 \pi } { 6 } , \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }
D) x=π4,3π4,5π4,7π4x = \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 }
E) x=π3,2π3,4π3,5π3x = \frac { \pi } { 3 } , \frac { 2 \pi } { 3 } , \frac { 4 \pi } { 3 } , \frac { 5 \pi } { 3 }

Correct Answer

verifed

verified

Use the graph below of the function to approximate the solutions to 3cos⁡(2x) −cos⁡(x) =03 \cos ( 2 x ) - \cos ( x ) = 0 in the interval [0,2π) [ 0,2 \pi ) . Round your answers to one decimal. Use the graph below of the function to approximate the solutions to 3 \cos ( 2 x ) - \cos ( x ) = 0 in the interval [ 0,2 \pi ) . Round your answers to one decimal. A) 0.7,2.0,1.5,4.8 B) 2.0,1.5,4.8,5.6 C) 2.0,2.2,4.0,5.6 D) 0.7,2.2,4.0,5.6 E) 0.7,1.5,4.0,6.3


A) 0.7,2.0,1.5,4.80.7,2.0,1.5,4.8
B) 2.0,1.5,4.8,5.62.0,1.5,4.8,5.6
C) 2.0,2.2,4.0,5.62.0,2.2,4.0,5.6
D) 0.7,2.2,4.0,5.60.7,2.2,4.0,5.6
E) 0.7,1.5,4.0,6.30.7,1.5,4.0,6.3

Correct Answer

verifed

verified

Verify the identity shown below. (1+cot⁡2θ)tan⁡2θ=sec⁡2θ\left( 1 + \cot ^ { 2 } \theta \right) \tan ^ { 2 } \theta = \sec ^ { 2 } \theta

Correct Answer

verifed

verified

None...

View Answer

Which of the following is a solution to the given equation? 2sin⁡x−1=02 \sin x - 1 = 0


A) x=7π6x = \frac { 7 \pi } { 6 }
B) x=2π3x = \frac { 2 \pi } { 3 }
C) x=3π4x = \frac { 3 \pi } { 4 }
D) x=5π6x = \frac { 5 \pi } { 6 }
E) x=7π4x = \frac { 7 \pi } { 4 }

Correct Answer

verifed

verified

Factor; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent. tan⁡3x−tan⁡2x+tan⁡x−1\tan ^ { 3 } x - \tan ^ { 2 } x + \tan x - 1


A) sin⁡x−cos⁡xcos⁡3x\frac { \sin x - \cos x } { \cos ^ { 3 } x }
B) sec⁡2x(sin⁡x−cos⁡xcos⁡x) \sec ^ { 2 } x \left( \frac { \sin x - \cos x } { \cos x } \right)
C) sin⁡xcos⁡3x−sec⁡2x\frac { \sin x } { \cos ^ { 3 } x } - \sec ^ { 2 } x
D) tan⁡xsec⁡2x−sec⁡2x\tan x \sec ^ { 2 } x - \sec ^ { 2 } x
E) sec⁡2x−tan⁡2x\sec ^ { 2 } x - \tan ^ { 2 } x

Correct Answer

verifed

verified

If csc⁡x=433\csc x = \frac { 4 \sqrt { 3 } } { 3 } and cos⁡x<0\cos x < 0 , evaluate the function below. sec⁡x\sec x


A) sec⁡x=43\sec x = \frac { 4 } { \sqrt { 3 } }
B) sec⁡x=−34\sec x = - \frac { \sqrt { 3 } } { 4 }
C) sec⁡x=−41313\sec x = - \frac { 4 \sqrt { 13 } } { 13 }
D) sec⁡x=−393\sec x = - \frac { \sqrt { 39 } } { 3 }
E) sec⁡x=393\sec x = \frac { \sqrt { 39 } } { 3 }

Correct Answer

verifed

verified

Which of the following is a solution to the given equation? 2cos⁡x+3=02 \cos x + \sqrt { 3 } = 0


A) x=2π3x = \frac { 2 \pi } { 3 }
B) x=π4x = \frac { \pi } { 4 }
C) x=π6x = \frac { \pi } { 6 }
D) x=7π6x = \frac { 7 \pi } { 6 }
E) x=7π4x = \frac { 7 \pi } { 4 }

Correct Answer

verifed

verified

Use the half-angle formula to simplify the given expression. 1+cos⁡16x2\sqrt { \frac { 1 + \cos 16 x } { 2 } }


A) cos⁡32x\cos 32 x
B) cos⁡8x\cos 8 x
C) cos⁡16x\cos 16 x
D) cos⁡64x\cos 64 x
E) cos⁡4x\cos 4 x

Correct Answer

verifed

verified

Showing 41 - 60 of 120

Related Exams

Exam 1

Functions and Their Graphs

120 Questions

Exam 2

Polynomial and Rational Functions

120 Questions

Exam 3

Exponential and Logarithmic Functions

120 Questions

Exam 4

Trigonometric Functions

120 Questions

Exam 6

Additional Topics in Trigonometry

120 Questions

Exam 7

Linear Systems and Matrices

120 Questions

Exam 8

Sequences, Series, and Probability

118 Questions

Exam 9

Topics in Analytic Geometry

120 Questions

Exam 10

Analytic Geometry in Three Dimensions

120 Questions

Exam 11

Limits and an Introduction to Calculus

120 Questions

Show Answer