Question 1

Give the amplitude or period as requested.
-Period of $y = \sin 3 x$

Accepted Answer

A)  $2 \pi$ 
B)  $\frac { 2 \pi } { 3 }$ 
C)  3 
D)  1 
A)  $2 \pi$ 
B)  $\frac { 2 \pi } { 3 }$ 
C)  3 
D)  1

Question 2

Graph the function over a one-period interval.
-The path of a projectile fired at an inclination $\theta$ to the horizontal with an initial speed $\mathrm { v } _ { \mathrm { O } }$ is a parabola. The range $\mathrm { R }$ of the projectile, the horizontal distance that the projectile travels, is found by the formula $\mathrm { R } = \frac { \mathrm { v } _ { \mathrm { O } } { } ^ { 2 } \sin 2 \theta } { \mathrm { g } }$ where $\mathrm { g } = 32.2$ feet per second per second or $\mathrm { g } = 9.8$ meters per second per second. Find the range of a projectile fired with an initial velocity of 146 feet per second at an angle of $27 ^ { \circ }$ to the horizontal. Round your answer to two decimal places.

Accepted Answer

A)  $535.56 \mathrm { ft }$ 
B)  $535.46 \mathrm { ft }$ 
C)  $300.54 \mathrm { ft }$ 
D)  $601.07 \mathrm { ft }$ 
A)  $535.56 \mathrm { ft }$ 
B)  $535.46 \mathrm { ft }$ 
C)  $300.54 \mathrm { ft }$ 
D)  $601.07 \mathrm { ft }$

Question 3

Use a table or a calculator to evaluate the function. Round to four decimal places.
-$\cot 0.2265$

Accepted Answer

A)  1.0262 
B)  4.3393 
C)  0.2305 
D)  0.9745 
A)  1.0262 
B)  4.3393 
C)  0.2305 
D)  0.9745

Question 4

Graph the function over a one-period interval.
-$$y = \frac { 1 } { 2 } \sin ( x + \pi )$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 5

Graph the function.
-$$y = \frac { 1 } { 2 } \cos \frac { 2 } { 3 } x$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 6

Use a table or a calculator to evaluate the function. Round to four decimal places.
-$$\sec 0.1769$$

Accepted Answer

A)  0.1760 
B)  1.0159 
C)  0.9844 
D)  0.1788 
A)  0.1760 
B)  1.0159 
C)  0.9844 
D)  0.1788

Question 7

Approximate the length using the formula for arc length. Round to the nearest meter.
-A tree $490 \mathrm {~m}$ away subtends an angle of $2 ^ { \circ }$. Find the height of the tree.

Accepted Answer

A)  $14 \mathrm {~m}$ 
B)  $37 \mathrm {~m}$ 
C)  $17 \mathrm {~m}$ 
D)  $34 \mathrm {~m}$ 
A)  $14 \mathrm {~m}$ 
B)  $37 \mathrm {~m}$ 
C)  $17 \mathrm {~m}$ 
D)  $34 \mathrm {~m}$

Question 8

Graph the function.
-$y=-2 \cos x$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 9

Graph the function over a one-period interval.
-$$y = 4 + 3 \sin ( x - \pi )$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 10

Use a table or a calculator to evaluate the function. Round to four decimal places.
-$$\tan 0.2667$$

Accepted Answer

A)  0.2732 
B)  0.9646 
C)  0.2635 
D)  1.0366 
A)  0.2732 
B)  0.9646 
C)  0.2635 
D)  1.0366

Question 11

Graph the function.
-$$y = \frac { 5 } { 2 } \csc \left( \frac { 4 } { 5 } x - \frac { \pi } { 4 } \right)$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 12

Find the phase shift of the function.
-$$y = \sin \left( x + \frac { \pi } { 4 } \right)$$

Accepted Answer

A)  $\frac { \pi } { 4 }$ units down 
B)  $\frac { \pi } { 4 }$ units to the right 
C)  $\frac { \pi } { 4 }$ units up 
D)  $\frac { \pi } { 4 }$ units to the left 
A)  $\frac { \pi } { 4 }$ units down 
B)  $\frac { \pi } { 4 }$ units to the right 
C)  $\frac { \pi } { 4 }$ units up 
D)  $\frac { \pi } { 4 }$ units to the left

Question 13

The function graphed is of the form y $$y = a \sin b x \text { or } y = a \cos b x , \text { where } b > 0$$ Determine the equation of the graph.
-

Accepted Answer

A)  $y = 5 \sin ( 3 x )$ 
B)  $y = 5 \cos \left( \frac { 1 } { 3 } x \right)$ 
C)  $y = 3 \sin \left( \frac { 1 } { 5 } x \right)$ 
D)  $y = 5 \cos ( 3 x )$ 
A)  $y = 5 \sin ( 3 x )$ 
B)  $y = 5 \cos \left( \frac { 1 } { 3 } x \right)$ 
C)  $y = 3 \sin \left( \frac { 1 } { 5 } x \right)$ 
D)  $y = 5 \cos ( 3 x )$

Question 14

Find the exact value of s in the given interval that has the given circular function value.
-$$\left[ \frac { 3 \pi } { 2 } , 2 \pi \right] ; \cos s = \frac { 1 } { 2 }$$

Accepted Answer

A)  $s = \frac { 7 \pi } { 4 }$ 
B)  $s = \frac { 5 \pi } { 3 }$ 
C)  $s = \frac { 11 \pi } { 6 }$ 
D)  $s = \frac { \pi } { 3 }$ 
A)  $s = \frac { 7 \pi } { 4 }$ 
B)  $s = \frac { 5 \pi } { 3 }$ 
C)  $s = \frac { 11 \pi } { 6 }$ 
D)  $s = \frac { \pi } { 3 }$

Question 15

Is it correct to say that the value of c ? Explain your answer. $\cos 30 = \frac { \sqrt { 3 } } { 2 }$

Accepted Answer

No, it is not correct because

Question 16

The figure shows an angle $$\theta$$ in standard position with its terminal side intersecting the unit circle. Evaluate the indicated
circular function value of $\theta$
-Find $\tan \theta$

Accepted Answer

A)  $- \frac { 24 } { 7 }$ 
B)  $- \frac { 25 } { 7 }$ 
C)  $\frac { 25 } { 24 }$ 
D)  $- \frac { 7 } { 24 }$ 
A)  $- \frac { 24 } { 7 }$ 
B)  $- \frac { 25 } { 7 }$ 
C)  $\frac { 25 } { 24 }$ 
D)  $- \frac { 7 } { 24 }$

Question 17

Graph the function over a one-period interval.
-A generator produces an alternating current according to the equation $\mathrm { I } = 24 \sin 14 \pi \mathrm { t }$, where $\mathrm { t }$ is time in seconds and I is the current in amperes. What is the smallest time $t$ such that $\mathrm { I } = 12 ?$

Accepted Answer

A)  $\frac { 1 } { 84 } \sec$ 
B)  $\frac { 1 } { 28 } \mathrm { sec }$ 
C)  $\frac { 1 } { 56 } \mathrm { sec }$ 
D)  $\frac { 1 } { 42 } \mathrm { sec }$ 
A)  $\frac { 1 } { 84 } \sec$ 
B)  $\frac { 1 } { 28 } \mathrm { sec }$ 
C)  $\frac { 1 } { 56 } \mathrm { sec }$ 
D)  $\frac { 1 } { 42 } \mathrm { sec }$

Question 18

Graph the function.
-$y=\frac{5}{6} \cot \left(\frac{3}{5} x-\frac{\pi}{4}\right)$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 19

If the radius of a circle is doubled, how is the length of the arc intercepted by a fixed central 
angle changed?

Accepted Answer

@#LAT-DLM& , so if r is double

Question 20

Find the exact circular function value.
-$$\sec \frac { - 3 \pi } { 4 }$$

Accepted Answer

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

Give the amplitude or period as requested. -Period of $y = \sin 3 x$

Use a table or a calculator to evaluate the function. Round to four decimal places. - $\cot 0.2265$

Graph the function over a one-period interval. - $y = \frac { 1 } { 2 } \sin ( x + \pi )$ $Graph the function over a one-period interval. - y = \frac { 1 } { 2 } \sin ( x + \pi )$

Graph the function. - $y = \frac { 1 } { 2 } \cos \frac { 2 } { 3 } x$ $Graph the function. - y = \frac { 1 } { 2 } \cos \frac { 2 } { 3 } x$

Use a table or a calculator to evaluate the function. Round to four decimal places. - $\sec 0.1769$

Approximate the length using the formula for arc length. Round to the nearest meter. -A tree $490 \mathrm {~m}$ away subtends an angle of $2 ^ { \circ }$ . Find the height of the tree.

Graph the function. - $y=-2 \cos x$ $Graph the function. - y=-2 \cos x$

Graph the function over a one-period interval. - $y = 4 + 3 \sin ( x - \pi )$ $Graph the function over a one-period interval. - y = 4 + 3 \sin ( x - \pi )$

Use a table or a calculator to evaluate the function. Round to four decimal places. - $\tan 0.2667$

Graph the function. - $y = \frac { 5 } { 2 } \csc \left( \frac { 4 } { 5 } x - \frac { \pi } { 4 } \right)$ $Graph the function. - y = \frac { 5 } { 2 } \csc \left( \frac { 4 } { 5 } x - \frac { \pi } { 4 } \right)$

Find the phase shift of the function. - $y = \sin \left( x + \frac { \pi } { 4 } \right)$

The function graphed is of the form y $y = a \sin b x \text { or } y = a \cos b x , \text { where } b > 0$ Determine the equation of the graph. - $The function graphed is of the form y y = a \sin b x \text { or } y = a \cos b x , \text { where } b > 0 Determine the equation of the graph. -$

Find the exact value of s in the given interval that has the given circular function value. - $\left[ \frac { 3 \pi } { 2 } , 2 \pi \right] ; \cos s = \frac { 1 } { 2 }$

Is it correct to say that the value of c ? Explain your answer. $\cos 30 = \frac { \sqrt { 3 } } { 2 }$

Graph the function. - $y=\frac{5}{6} \cot \left(\frac{3}{5} x-\frac{\pi}{4}\right)$ $Graph the function. - y=\frac{5}{6} \cot \left(\frac{3}{5} x-\frac{\pi}{4}\right)$

If the radius of a circle is doubled, how is the length of the arc intercepted by a fixed central angle changed?

Find the exact circular function value. - $\sec \frac { - 3 \pi } { 4 }$

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Exam 7: The Circular Functions and Their Graphs

Give the amplitude or period as requested. -Period of y=sin⁡3xy = \sin 3 xy=sin3x

Use a table or a calculator to evaluate the function. Round to four decimal places. - cot⁡0.2265\cot 0.2265cot0.2265

Graph the function over a one-period interval. - y=12sin⁡(x+π)y = \frac { 1 } { 2 } \sin ( x + \pi )y=21​sin(x+π)

Graph the function. - y=12cos⁡23xy = \frac { 1 } { 2 } \cos \frac { 2 } { 3 } xy=21​cos32​x

Use a table or a calculator to evaluate the function. Round to four decimal places. - sec⁡0.1769\sec 0.1769sec0.1769

Approximate the length using the formula for arc length. Round to the nearest meter. -A tree 490 m490 \mathrm {~m}490 m away subtends an angle of 2∘2 ^ { \circ }2∘ . Find the height of the tree.

Graph the function. - y=−2cos⁡xy=-2 \cos xy=−2cosx

Graph the function over a one-period interval. - y=4+3sin⁡(x−π)y = 4 + 3 \sin ( x - \pi )y=4+3sin(x−π)

Use a table or a calculator to evaluate the function. Round to four decimal places. - tan⁡0.2667\tan 0.2667tan0.2667

Graph the function. - y=52csc⁡(45x−π4)y = \frac { 5 } { 2 } \csc \left( \frac { 4 } { 5 } x - \frac { \pi } { 4 } \right)y=25​csc(54​x−4π​)

Find the phase shift of the function. - y=sin⁡(x+π4)y = \sin \left( x + \frac { \pi } { 4 } \right)y=sin(x+4π​)

The function graphed is of the form y y=asin⁡bx or y=acos⁡bx, where b>0y = a \sin b x \text { or } y = a \cos b x , \text { where } b > 0y=asinbx or y=acosbx, where b>0 Determine the equation of the graph. -

Find the exact value of s in the given interval that has the given circular function value. - [3π2,2π];cos⁡s=12\left[ \frac { 3 \pi } { 2 } , 2 \pi \right] ; \cos s = \frac { 1 } { 2 }[23π​,2π];coss=21​

Is it correct to say that the value of c ? Explain your answer. cos⁡30=32\cos 30 = \frac { \sqrt { 3 } } { 2 }cos30=23​​

The figure shows an angle θ\thetaθ in standard position with its terminal side intersecting the unit circle. Evaluate the indicated circular function value of θ\thetaθ -Find tan⁡θ\tan \thetatanθ

Graph the function. - y=56cot⁡(35x−π4)y=\frac{5}{6} \cot \left(\frac{3}{5} x-\frac{\pi}{4}\right)y=65​cot(53​x−4π​)

If the radius of a circle is doubled, how is the length of the arc intercepted by a fixed central angle changed?

Find the exact circular function value. - sec⁡−3π4\sec \frac { - 3 \pi } { 4 }sec4−3π​

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Give the amplitude or period as requested. -Period of $y = \sin 3 x$

Use a table or a calculator to evaluate the function. Round to four decimal places. - $\cot 0.2265$

Graph the function over a one-period interval. - $y = \frac { 1 } { 2 } \sin ( x + \pi )$ $Graph the function over a one-period interval. - y = \frac { 1 } { 2 } \sin ( x + \pi )$

Graph the function. - $y = \frac { 1 } { 2 } \cos \frac { 2 } { 3 } x$ $Graph the function. - y = \frac { 1 } { 2 } \cos \frac { 2 } { 3 } x$

Use a table or a calculator to evaluate the function. Round to four decimal places. - $\sec 0.1769$

Approximate the length using the formula for arc length. Round to the nearest meter. -A tree $490 \mathrm {~m}$ away subtends an angle of $2 ^ { \circ }$ . Find the height of the tree.

Graph the function. - $y=-2 \cos x$ $Graph the function. - y=-2 \cos x$

Graph the function over a one-period interval. - $y = 4 + 3 \sin ( x - \pi )$ $Graph the function over a one-period interval. - y = 4 + 3 \sin ( x - \pi )$

Use a table or a calculator to evaluate the function. Round to four decimal places. - $\tan 0.2667$

Graph the function. - $y = \frac { 5 } { 2 } \csc \left( \frac { 4 } { 5 } x - \frac { \pi } { 4 } \right)$ $Graph the function. - y = \frac { 5 } { 2 } \csc \left( \frac { 4 } { 5 } x - \frac { \pi } { 4 } \right)$

Find the phase shift of the function. - $y = \sin \left( x + \frac { \pi } { 4 } \right)$

The function graphed is of the form y $y = a \sin b x \text { or } y = a \cos b x , \text { where } b > 0$ Determine the equation of the graph. - $The function graphed is of the form y y = a \sin b x \text { or } y = a \cos b x , \text { where } b > 0 Determine the equation of the graph. -$

Find the exact value of s in the given interval that has the given circular function value. - $\left[ \frac { 3 \pi } { 2 } , 2 \pi \right] ; \cos s = \frac { 1 } { 2 }$

Is it correct to say that the value of c ? Explain your answer. $\cos 30 = \frac { \sqrt { 3 } } { 2 }$

Graph the function. - $y=\frac{5}{6} \cot \left(\frac{3}{5} x-\frac{\pi}{4}\right)$ $Graph the function. - y=\frac{5}{6} \cot \left(\frac{3}{5} x-\frac{\pi}{4}\right)$

Find the exact circular function value. - $\sec \frac { - 3 \pi } { 4 }$