Question 1

Rewrite in terms of sine and cosine, and simplify the expression: $\sec A \csc A - \tan A - \cot A$

Accepted Answer

A)  $\sec A$ 
B)  $0$ 
C)  $\cot A$ 
D)  $1$ 
E)  $\tan A$ 
A)  $\sec A$ 
B)  $0$ 
C)  $\cot A$ 
D)  $1$ 
E)  $\tan A$

Question 2

Evaluate the expressions using reference angles. $\csc \left( - 840 ^ { \circ } \right)$ $\cot \left( - 840 ^ { \circ } \right)$

Accepted Answer

A)  $\csc \left( - 840 ^ { \circ } \right) = - \frac { 2 \sqrt { 2 } } { 3 }$ $\cot \left( - 840 ^ { \circ } \right) = \frac { \sqrt { 2 } } { 2 }$ 
B)  $\csc \left( - 840 ^ { \circ } \right) = \frac { \sqrt { 3 } } { 3 }$ $\cot \left( - 840 ^ { \circ } \right) = \frac { \sqrt { 3 } } { 3 }$ 
C)  $\csc \left( - 840 ^ { \circ } \right) = - \frac { \sqrt { 2 } } { 2 }$ $\cot \left( - 840 ^ { \circ } \right) = \frac { \sqrt { 2 } } { 3 }$ 
D)  $\csc \left( - 840 ^ { \circ } \right) = - \frac { 1 } { 3 }$ $\cot \left( - 840 ^ { \circ } \right) = \frac { 1 } { 3 }$ 
E)  $\csc \left( - 840 ^ { \circ } \right) = - \frac { 2 \sqrt { 3 } } { 3 }$ $\cot \left( - 840 ^ { \circ } \right) = \frac { \sqrt { 3 } } { 3 }$ 
A)  $\csc \left( - 840 ^ { \circ } \right) = - \frac { 2 \sqrt { 2 } } { 3 }$ $\cot \left( - 840 ^ { \circ } \right) = \frac { \sqrt { 2 } } { 2 }$ 
B)  $\csc \left( - 840 ^ { \circ } \right) = \frac { \sqrt { 3 } } { 3 }$ $\cot \left( - 840 ^ { \circ } \right) = \frac { \sqrt { 3 } } { 3 }$ 
C)  $\csc \left( - 840 ^ { \circ } \right) = - \frac { \sqrt { 2 } } { 2 }$ $\cot \left( - 840 ^ { \circ } \right) = \frac { \sqrt { 2 } } { 3 }$ 
D)  $\csc \left( - 840 ^ { \circ } \right) = - \frac { 1 } { 3 }$ $\cot \left( - 840 ^ { \circ } \right) = \frac { 1 } { 3 }$ 
E)  $\csc \left( - 840 ^ { \circ } \right) = - \frac { 2 \sqrt { 3 } } { 3 }$ $\cot \left( - 840 ^ { \circ } \right) = \frac { \sqrt { 3 } } { 3 }$

Question 3

Use the definition $\theta = \frac { s } { r }$ to determine the radian measure of the angle.

Accepted Answer

A)  $\theta = 4.05$ radians 
B)  $\theta = 3$ radians 
C)  $\theta = 3.08$ radians 
D)  $\theta$ radians 
E)  $\theta = 3.15$ radians 
A)  $\theta = 4.05$ radians 
B)  $\theta = 3$ radians 
C)  $\theta = 3.08$ radians 
D)  $\theta$ radians 
E)  $\theta = 3.15$ radians

Question 4

You are given the rate of rotation of a wheel as well as its radius. Determine the following: (a) the angular speed, in units of radians/sec; (b) the linear speed, in units of cm/sec, of a point on the circumference of the wheel; (c) and the linear speed, in cm/sec, of a point halfway between the center of the wheel and the circumference. $$520$$ rpm; $r = 45$ cm

Accepted Answer

A)  (a) 156 $\pi$ radian/sec,
   (b) 780 $\pi$ cm/sec,
   (c) 390 $\pi$ cm/sec 
B)  (a) $166 ~\pi ~\mathrm { radian } / \mathrm { sec }$
(b) 1,278 $\pi$ cm/sec,
(c) 400 $\pi$ cm/sec 
C)  (a) $\frac { 52 \pi } { 11 }$ radian/sec,
(b) 1,248 $\pi$ cm/sec,
(c) 624 $\pi$ cm/sec 
D)  (a) 520 $\pi$ radian/sec,
(b) 780 $\pi$ cm/sec,
(c) 1,560 $\pi$ cm/sec 
E)  (a) $\frac { 52 \pi } { 3 }$ radian/sec,
(b) 780 $\pi$ cm/sec,
(c) 390 $\pi$ cm/sec 
A)  (a) 156 $\pi$ radian/sec,
   (b) 780 $\pi$ cm/sec,
   (c) 390 $\pi$ cm/sec 
B)  (a) $166 ~\pi ~\mathrm { radian } / \mathrm { sec }$
(b) 1,278 $\pi$ cm/sec,
(c) 400 $\pi$ cm/sec 
C)  (a) $\frac { 52 \pi } { 11 }$ radian/sec,
(b) 1,248 $\pi$ cm/sec,
(c) 624 $\pi$ cm/sec 
D)  (a) 520 $\pi$ radian/sec,
(b) 780 $\pi$ cm/sec,
(c) 1,560 $\pi$ cm/sec 
E)  (a) $\frac { 52 \pi } { 3 }$ radian/sec,
(b) 780 $\pi$ cm/sec,
(c) 390 $\pi$ cm/sec

Question 5

Suppose that $A B C$ is a right triangle with $\angle C = 90 ^ { \circ }$ . If $A C = 12$ and $B C = 6$ , find the quantities. $\cos A , \sin A , \tan A , \sec B , \csc B , \cot B$ .

Accepted Answer

A)  $\cos A = \frac { 2 \sqrt { 5 } } { 5 }$ , $\sec B = 5$ , $\tan A = \frac { 1 } { 2 }$ , $\sin A = \frac { \sqrt { 5 } } { 5 }$ , $\csc B = \frac { 1 } { 5 }$ , $\cot B = \frac { 1 } { 2 }$ 
B)  $\cos A = \frac { 2 \sqrt { 5 } } { 5 }$ , $\sec B = \sqrt { 5 }$ , $\tan A = 2$ , $\sin A = \frac { \sqrt { 5 } } { 5 }$ , $\csc B = \frac { \sqrt { 5 } } { 2 }$ , $\cot B = \frac { 1 } { 2 }$ 
C)  $\cos A = \frac { 2 \sqrt { 5 } } { 5 }$ , $\sec B = \frac { \sqrt { 5 } } { 2 }$ , $\tan A = \frac { 1 } { 2 }$ , $\sin A = \frac { \sqrt { 5 } } { 5 }$ , $\csc B = \sqrt { 5 }$ , $\cot B = 2$ 
D)  $\cos A = \frac { 2 \sqrt { 5 } } { 5 }$ , $\sec B = \sqrt { 5 }$ , $\tan A = \frac { 1 } { 2 }$ , $\sin A = \frac { \sqrt { 5 } } { 5 }$ , $\csc B = \frac { \sqrt { 5 } } { 2 }$ , $\cot B = \frac { 1 } { 2 }$ 
E)  $\cos A = \frac { 2 \sqrt { 5 } } { 5 }$ , $\sec B = \sqrt { 5 }$ , $\tan A = \frac { 1 } { 2 }$ , $\sin A = \frac { \sqrt { 5 } } { 5 }$ , $\csc B = \frac { \sqrt { 5 } } { 2 }$ , $\cot B = 2$ 
A)  $\cos A = \frac { 2 \sqrt { 5 } } { 5 }$ , $\sec B = 5$ , $\tan A = \frac { 1 } { 2 }$ , $\sin A = \frac { \sqrt { 5 } } { 5 }$ , $\csc B = \frac { 1 } { 5 }$ , $\cot B = \frac { 1 } { 2 }$ 
B)  $\cos A = \frac { 2 \sqrt { 5 } } { 5 }$ , $\sec B = \sqrt { 5 }$ , $\tan A = 2$ , $\sin A = \frac { \sqrt { 5 } } { 5 }$ , $\csc B = \frac { \sqrt { 5 } } { 2 }$ , $\cot B = \frac { 1 } { 2 }$ 
C)  $\cos A = \frac { 2 \sqrt { 5 } } { 5 }$ , $\sec B = \frac { \sqrt { 5 } } { 2 }$ , $\tan A = \frac { 1 } { 2 }$ , $\sin A = \frac { \sqrt { 5 } } { 5 }$ , $\csc B = \sqrt { 5 }$ , $\cot B = 2$ 
D)  $\cos A = \frac { 2 \sqrt { 5 } } { 5 }$ , $\sec B = \sqrt { 5 }$ , $\tan A = \frac { 1 } { 2 }$ , $\sin A = \frac { \sqrt { 5 } } { 5 }$ , $\csc B = \frac { \sqrt { 5 } } { 2 }$ , $\cot B = \frac { 1 } { 2 }$ 
E)  $\cos A = \frac { 2 \sqrt { 5 } } { 5 }$ , $\sec B = \sqrt { 5 }$ , $\tan A = \frac { 1 } { 2 }$ , $\sin A = \frac { \sqrt { 5 } } { 5 }$ , $\csc B = \frac { \sqrt { 5 } } { 2 }$ , $\cot B = 2$

Rewrite in terms of sine and cosine, and simplify the expression: $\sec A \csc A - \tan A - \cot A$

Evaluate the expressions using reference angles. $\csc \left( - 840 ^ { \circ } \right)$ $\cot \left( - 840 ^ { \circ } \right)$

Use the definition $\theta = \frac { s } { r }$ to determine the radian measure of the angle. $Use the definition \theta = \frac { s } { r } to determine the radian measure of the angle.$

Suppose that $A B C$ is a right triangle with $\angle C = 90 ^ { \circ }$ . If $A C = 12$ and $B C = 6$ , find the quantities. $\cos A , \sin A , \tan A , \sec B , \csc B , \cot B$ .

Fundamentals

Equations and Inequalities

Functions

Polynomial and Rational Functions Applications to Optimization

Exponential and Logarithmic Functions

An Introduction to Trigonometry Via Right Triangles

Graphs of the Trigonometric Functions

Analytical Trigonometry

Additional Topics in Trigonometry

Systems of Equations

The Conic Sections

Roots of Polynomial Equations

Additional Topics in Algebra

Filters

Exam 7: The Trigonometric Functions

Rewrite in terms of sine and cosine, and simplify the expression: sec⁡Acsc⁡A−tan⁡A−cot⁡A\sec A \csc A - \tan A - \cot AsecAcscA−tanA−cotA

Evaluate the expressions using reference angles. csc⁡(−840∘)\csc \left( - 840 ^ { \circ } \right)csc(−840∘) cot⁡(−840∘)\cot \left( - 840 ^ { \circ } \right)cot(−840∘)

Use the definition θ=sr\theta = \frac { s } { r }θ=rs​ to determine the radian measure of the angle.

Suppose that ABCA B CABC is a right triangle with ∠C=90∘\angle C = 90 ^ { \circ }∠C=90∘ . If AC=12A C = 12AC=12 and BC=6B C = 6BC=6 , find the quantities. cos⁡A,sin⁡A,tan⁡A,sec⁡B,csc⁡B,cot⁡B\cos A , \sin A , \tan A , \sec B , \csc B , \cot BcosA,sinA,tanA,secB,cscB,cotB .

Fundamentals

Equations and Inequalities

Functions

Polynomial and Rational Functions Applications to Optimization

Exponential and Logarithmic Functions

An Introduction to Trigonometry Via Right Triangles

Graphs of the Trigonometric Functions

Analytical Trigonometry

Additional Topics in Trigonometry

Systems of Equations

The Conic Sections

Roots of Polynomial Equations

Additional Topics in Algebra

Filters

Rewrite in terms of sine and cosine, and simplify the expression: $\sec A \csc A - \tan A - \cot A$

Evaluate the expressions using reference angles. $\csc \left( - 840 ^ { \circ } \right)$ $\cot \left( - 840 ^ { \circ } \right)$

Use the definition $\theta = \frac { s } { r }$ to determine the radian measure of the angle. $Use the definition \theta = \frac { s } { r } to determine the radian measure of the angle.$

Suppose that $A B C$ is a right triangle with $\angle C = 90 ^ { \circ }$ . If $A C = 12$ and $B C = 6$ , find the quantities. $\cos A , \sin A , \tan A , \sec B , \csc B , \cot B$ .