Question 1

Find $\sec \theta$ , and $\csc \theta$ given that $\cot \theta = - \frac { 4 } { 3 }$ and $\sec \theta > 0$

Accepted Answer

A)  $\sec \theta = \frac { \sqrt { 7 } } { 4 }$
, $ \csc \theta=-\frac{5}{3} $ 
B)  $ \sec \theta=\frac{5}{4} $
, $\csc = - \frac { \sqrt { 7 } } { 3 }$ 
C)  $ \sec \theta=\frac{5}{4} $
, $ \csc \theta=-\frac{5}{3} $ 
D)  $ \sec \theta=\frac{5}{3} $
, $ \csc \theta=-\frac{5}{3} $ 
E)  $ \sec \theta=\frac{5}{4} $
, $ \csc \theta=\frac{5}{3} $ 
A)  $\sec \theta = \frac { \sqrt { 7 } } { 4 }$
, $ \csc \theta=-\frac{5}{3} $ 
B)  $ \sec \theta=\frac{5}{4} $
, $\csc = - \frac { \sqrt { 7 } } { 3 }$ 
C)  $ \sec \theta=\frac{5}{4} $
, $ \csc \theta=-\frac{5}{3} $ 
D)  $ \sec \theta=\frac{5}{3} $
, $ \csc \theta=-\frac{5}{3} $ 
E)  $ \sec \theta=\frac{5}{4} $
, $ \csc \theta=\frac{5}{3} $ C

Question 2

Find the values of $\sec \theta$ and $\cot \theta$If the point $( - 3,4 )$Is on the terminal side of $\theta$

Accepted Answer

A)  $\sec \theta = - \frac { 4 } { 3 }$
, $\cot \theta = - \frac { 3 } { 4 }$ 
B)  $\sec \theta = - \frac { 5 } { 3 }$
, $\cot \theta = - \frac { 3 } { 4 }$ 
C)  $\sec \theta = - \frac { \sqrt { 7 } } { 3 }$
, $\cot \theta = \frac { 5 } { 4 }$ 
D)  $\sec \theta = - \frac { \sqrt { 7 } } { 3 }$
, $\cot \theta = - \frac { 3 } { 4 }$ 
E)  $\sec \theta = - \frac { 5 } { 3 }$
, $\cot \theta = \frac { 4 } { 3 }$ 
A)  $\sec \theta = - \frac { 4 } { 3 }$
, $\cot \theta = - \frac { 3 } { 4 }$ 
B)  $\sec \theta = - \frac { 5 } { 3 }$
, $\cot \theta = - \frac { 3 } { 4 }$ 
C)  $\sec \theta = - \frac { \sqrt { 7 } } { 3 }$
, $\cot \theta = \frac { 5 } { 4 }$ 
D)  $\sec \theta = - \frac { \sqrt { 7 } } { 3 }$
, $\cot \theta = - \frac { 3 } { 4 }$ 
E)  $\sec \theta = - \frac { 5 } { 3 }$
, $\cot \theta = \frac { 4 } { 3 }$ B

Question 3

A pilot sets out from an airport and heads in the direction N $30 ^ { \circ }$ W, flying at a constant speed of $305$ mi/h. Forty-five minutes later the pilot makes a course and speed correction and now heads in the direction N $50 ^ { \circ }$ W and reduces her speed to $175$ mi/h. Half an hour later, engine trouble forces her to make an emergency landing. Find the distance between the airport and the final landing point.

Accepted Answer

Forty-five minutes after take off the pilot has traveled $228.75$ miles and $87.5$ 
miles after her course correction. The distance between the airport and the final landing point can be found by the following: $x ^ { 2 } = ( 228.75 ) ^ { 2 } + ( 87.5 ) ^ { 2 } - 2 ( 228.75 ) ( 87.5 ) \cos 160 ^ { \circ } \approx 97600$ $\Rightarrow$ $x \approx \sqrt { 97600 } \approx 312.41 \mathrm { mi }$

Question 4

Find the exact value of the expression. $\tan \left( \sin ^ { - 1 } \frac { 3 } { 5 } \right)$

Accepted Answer

A)  $3 / 5$ 
B)  $5 / 3$ 
C)  $- 3 / 5$ 
D)  $- 5 / 3$ 
E) none of these 
A)  $3 / 5$ 
B)  $5 / 3$ 
C)  $- 3 / 5$ 
D)  $- 5 / 3$ 
E) none of these

Question 5

Find the length of an arc of a circle of radius $12$ 
ft if the arc subtends a central angle of $135 ^ { \circ }$ .

Accepted Answer

The answer of Find the length of an arc of...

Question 6

Find the area of a sector with central angle $5 \pi / 4$ in a circle with radius $0.5$ m.

Accepted Answer

The answer of Find the area of a sector with...

Question 7

If $\sin \theta = \frac { \sqrt { 3 } } { 2 }$ for $\theta$
In quadrant I, find $\tan \theta + \sec \theta$

Accepted Answer

A)  $\sqrt { 3 } - 3$ 
B)  $\sqrt { 3 } + 1$ 
C)  $\sqrt { 3 } + 2$ 
D)  $\sqrt { 2 } + 3$ 
E)  $3 \sqrt { 2 }$ 
A)  $\sqrt { 3 } - 3$ 
B)  $\sqrt { 3 } + 1$ 
C)  $\sqrt { 3 } + 2$ 
D)  $\sqrt { 2 } + 3$ 
E)  $3 \sqrt { 2 }$

Question 8

Find the measure of the central angle $\theta$  in a circle of radius 8 ft if the angle is subtended by an arc of length 7 ft.

Accepted Answer

The answer of Find the measure of the central angle...

Question 9

Find $\sin \theta$ and $\cos \theta$ given that $\sec \theta = - 2$ and $\tan \theta > 0$ .

Accepted Answer

The answer of Find $\sin \theta$ and $\cos \theta$ given...

Question 10

Rewrite the expression as an algebraic expression in x. $\sin \left( \cos ^ { - 1 } x \right)$

Accepted Answer

A)  $1 - x$ 
B)  $1 - x ^ { 2 }$ 
C)  $\sqrt { 1 - x ^ { 2 } }$ 
D)  $\frac { \sqrt { x ^ { 2 } - 1 } } { x }$ 
E)  $\frac { x } { \sqrt { x ^ { 2 } - 1 } }$ 
A)  $1 - x$ 
B)  $1 - x ^ { 2 }$ 
C)  $\sqrt { 1 - x ^ { 2 } }$ 
D)  $\frac { \sqrt { x ^ { 2 } - 1 } } { x }$ 
E)  $\frac { x } { \sqrt { x ^ { 2 } - 1 } }$

Question 11

A 86-ft tree casts a shadow that is 110 ft long. What is the angle of elevation of the sun? Round the answer to two decimal places.

Accepted Answer

The answer of A 86-ft tree casts a shadow that...

Question 12

Find the reference angle for the given angles
a) $- 202 ^ { \circ }$

b) $\frac { 19 \pi } { 6 }$

Accepted Answer

The answer of Find the reference angle for the given...

Question 13

Rewrite the expression as an algebraic expression in x. $\sin \left( \cos ^ { - 1 } x \right)$

Accepted Answer

A)  $1 - x$ 
B)  $1 - x ^ { 2 }$ 
C)  $\sqrt { 1 - x ^ { 2 } }$ 
D)  $\frac { \sqrt { x ^ { 2 } - 1 } } { x }$ 
E)  $\frac { x } { \sqrt { x ^ { 2 } - 1 } }$ 
A)  $1 - x$ 
B)  $1 - x ^ { 2 }$ 
C)  $\sqrt { 1 - x ^ { 2 } }$ 
D)  $\frac { \sqrt { x ^ { 2 } - 1 } } { x }$ 
E)  $\frac { x } { \sqrt { x ^ { 2 } - 1 } }$

Question 14

Land on a small Caribbean island is valued at $\$ 45$ per square foot. What is the value of a triangular lot with sides of lengths $80$
Ft, $50$Ft, and $120$ Ft?

Accepted Answer

A)  $\$ 65,358$ 
B)  $\$ 216,000$ 
C)  $\$ 108,358$ 
D)  $\$ 55,000$ 
E)  $\$ 45,358$ 
A)  $\$ 65,358$ 
B)  $\$ 216,000$ 
C)  $\$ 108,358$ 
D)  $\$ 55,000$ 
E)  $\$ 45,358$

Question 15

Solve the triangle. $a = 72.5 , \quad \angle B = 60 ^ { \circ } , \quad \angle C = 83 ^ { \circ }$

Accepted Answer

A)  $\angle A = 37 ^ { \circ } , \quad b \approx 104.3 , \quad c \approx 119.6$ 
B)  $\angle A = 37 ^ { \circ } , \quad b \approx 103.1 , \quad c \approx 119.4$ 
C)  $\angle A = 37 ^ { \circ } , \quad b \approx 104.3 , \quad c \approx 117.6$ 
D)  $\angle A = 37 ^ { \circ } , b \approx 97 , \quad c \approx 119.6$ 
E)  none of these 
A)  $\angle A = 37 ^ { \circ } , \quad b \approx 104.3 , \quad c \approx 119.6$ 
B)  $\angle A = 37 ^ { \circ } , \quad b \approx 103.1 , \quad c \approx 119.4$ 
C)  $\angle A = 37 ^ { \circ } , \quad b \approx 104.3 , \quad c \approx 117.6$ 
D)  $\angle A = 37 ^ { \circ } , b \approx 97 , \quad c \approx 119.6$ 
E)  none of these

Question 16

Find the indicated angle $\theta$ .

Accepted Answer

The answer of Find the indicated angle $\theta$ . ...

Question 17

Sketch the triangle given by $\angle A = 23 ^ { \circ }$ , $\angle B = 78 ^ { \circ }$
, $c = 88$
, and solve it using the Law of Sines

Accepted Answer

A)  $\angle C = 79 ^ { \circ } , a = 88 , b = 25$ 
B)  $\angle C = 78 ^ { \circ } , a = 65 , b = 88$ 
C)  $\angle C = 23 , a = 37 , b = 88$ 
D)  $\angle C = 79 ^ { \circ } , a = 35 , b = 88$ 
E)  $\angle C = 101 ^ { \circ } , a = 35 , b = 40$ 
A)  $\angle C = 79 ^ { \circ } , a = 88 , b = 25$ 
B)  $\angle C = 78 ^ { \circ } , a = 65 , b = 88$ 
C)  $\angle C = 23 , a = 37 , b = 88$ 
D)  $\angle C = 79 ^ { \circ } , a = 35 , b = 88$ 
E)  $\angle C = 101 ^ { \circ } , a = 35 , b = 40$

Question 18

Find the side labeled x.

Accepted Answer

The answer of Find the side labeled x.  ...

Question 19

A $95 - \mathrm { t }$ tree casts a shadow that is $45$Ft long. What is the angle of elevation of the sun?

Accepted Answer

A)  $58.7 ^ { \circ }$ 
B)  $25.3 ^ { \circ }$ 
C)  $64.7 ^ { \circ }$ 
D)  $47.3 ^ { \circ }$ 
E)  $887 ^ { \circ }$ 
A)  $58.7 ^ { \circ }$ 
B)  $25.3 ^ { \circ }$ 
C)  $64.7 ^ { \circ }$ 
D)  $47.3 ^ { \circ }$ 
E)  $887 ^ { \circ }$

Question 20

Find the exact value of the expression. $\csc \left( \cos ^ { - 1 } \frac { 24 } { 25 } \right)$

Accepted Answer

A)  $28 ^ { \circ }$ 
B)  $16 ^ { \circ }$ 
C)  $- 1 ^ { \circ }$ 
D)  $88 ^ { \circ }$ 
E) none of these 
A)  $28 ^ { \circ }$ 
B)  $16 ^ { \circ }$ 
C)  $- 1 ^ { \circ }$ 
D)  $88 ^ { \circ }$ 
E) none of these

Find $\sec \theta$ , and $\csc \theta$ given that $\cot \theta = - \frac { 4 } { 3 }$ and $\sec \theta > 0$

Find the values of $\sec \theta$ and $\cot \theta$ If the point $( - 3,4 )$ Is on the terminal side of $\theta$

Find the exact value of the expression. $\tan \left( \sin ^ { - 1 } \frac { 3 } { 5 } \right)$

Find the length of an arc of a circle of radius $12$ ft if the arc subtends a central angle of $135 ^ { \circ }$ .

Find the area of a sector with central angle $5 \pi / 4$ in a circle with radius $0.5$ m.

If $\sin \theta = \frac { \sqrt { 3 } } { 2 }$ for $\theta$ In quadrant I, find $\tan \theta + \sec \theta$

Find the measure of the central angle $\theta$ in a circle of radius 8 ft if the angle is subtended by an arc of length 7 ft.

Find $\sin \theta$ and $\cos \theta$ given that $\sec \theta = - 2$ and $\tan \theta > 0$ .

Rewrite the expression as an algebraic expression in x. $\sin \left( \cos ^ { - 1 } x \right)$

A 86-ft tree casts a shadow that is 110 ft long. What is the angle of elevation of the sun? Round the answer to two decimal places.

Find the reference angle for the given angles a) $- 202 ^ { \circ }$ b) $\frac { 19 \pi } { 6 }$

Rewrite the expression as an algebraic expression in x. $\sin \left( \cos ^ { - 1 } x \right)$

Land on a small Caribbean island is valued at $\$ 45$ per square foot. What is the value of a triangular lot with sides of lengths $80$ Ft, $50$ Ft, and $120$ Ft?

Solve the triangle. $a = 72.5 , \quad \angle B = 60 ^ { \circ } , \quad \angle C = 83 ^ { \circ }$

Find the indicated angle $\theta$ . $Find the indicated angle \theta .$

Sketch the triangle given by $\angle A = 23 ^ { \circ }$ , $\angle B = 78 ^ { \circ }$ , $c = 88$ , and solve it using the Law of Sines

Find the side labeled x.

A $95 - \mathrm { t }$ tree casts a shadow that is $45$ Ft long. What is the angle of elevation of the sun?

Find the exact value of the expression. $\csc \left( \cos ^ { - 1 } \frac { 24 } { 25 } \right)$

Equations and Graphs

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Right Triangle Approach

Conic Sections

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections

Sequences and Series

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Filters

Exam 6: Trigonometric Functions: Unit Circle Approach

Find sec⁡θ\sec \thetasecθ , and csc⁡θ\csc \thetacscθ given that cot⁡θ=−43\cot \theta = - \frac { 4 } { 3 }cotθ=−34​ and sec⁡θ>0\sec \theta > 0secθ>0

Find the values of sec⁡θ\sec \thetasecθ and cot⁡θ\cot \thetacotθ If the point (−3,4)( - 3,4 )(−3,4) Is on the terminal side of θ\thetaθ

Find the exact value of the expression. tan⁡(sin⁡−135)\tan \left( \sin ^ { - 1 } \frac { 3 } { 5 } \right)tan(sin−153​)

Find the length of an arc of a circle of radius 121212 ft if the arc subtends a central angle of 135∘135 ^ { \circ }135∘ .

Find the area of a sector with central angle 5π/45 \pi / 45π/4 in a circle with radius 0.50.50.5 m.

If sin⁡θ=32\sin \theta = \frac { \sqrt { 3 } } { 2 }sinθ=23​​ for θ\thetaθ In quadrant I, find tan⁡θ+sec⁡θ\tan \theta + \sec \thetatanθ+secθ

Find the measure of the central angle θ\thetaθ in a circle of radius 8 ft if the angle is subtended by an arc of length 7 ft.

Find sin⁡θ\sin \thetasinθ and cos⁡θ\cos \thetacosθ given that sec⁡θ=−2\sec \theta = - 2secθ=−2 and tan⁡θ>0\tan \theta > 0tanθ>0 .

Rewrite the expression as an algebraic expression in x. sin⁡(cos⁡−1x)\sin \left( \cos ^ { - 1 } x \right)sin(cos−1x)

A 86-ft tree casts a shadow that is 110 ft long. What is the angle of elevation of the sun? Round the answer to two decimal places.

Find the reference angle for the given angles a) −202∘- 202 ^ { \circ }−202∘ b) 19π6\frac { 19 \pi } { 6 }619π​

Rewrite the expression as an algebraic expression in x. sin⁡(cos⁡−1x)\sin \left( \cos ^ { - 1 } x \right)sin(cos−1x)

Land on a small Caribbean island is valued at $45\$ 45$45 per square foot. What is the value of a triangular lot with sides of lengths 808080 Ft, 505050 Ft, and 120120120 Ft?

Solve the triangle. a=72.5,∠B=60∘,∠C=83∘a = 72.5 , \quad \angle B = 60 ^ { \circ } , \quad \angle C = 83 ^ { \circ }a=72.5,∠B=60∘,∠C=83∘

Find the indicated angle θ\thetaθ .

Sketch the triangle given by ∠A=23∘\angle A = 23 ^ { \circ }∠A=23∘ , ∠B=78∘\angle B = 78 ^ { \circ }∠B=78∘ , c=88c = 88c=88 , and solve it using the Law of Sines

Find the side labeled x.

A 95−t95 - \mathrm { t }95−t tree casts a shadow that is 454545 Ft long. What is the angle of elevation of the sun?

Find the exact value of the expression. csc⁡(cos⁡−12425)\csc \left( \cos ^ { - 1 } \frac { 24 } { 25 } \right)csc(cos−12524​)

Equations and Graphs

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Right Triangle Approach

Conic Sections

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections

Sequences and Series

Counting and Probability

Filters

Find $\sec \theta$ , and $\csc \theta$ given that $\cot \theta = - \frac { 4 } { 3 }$ and $\sec \theta > 0$

Find the values of $\sec \theta$ and $\cot \theta$ If the point $( - 3,4 )$ Is on the terminal side of $\theta$

Find the exact value of the expression. $\tan \left( \sin ^ { - 1 } \frac { 3 } { 5 } \right)$

Find the length of an arc of a circle of radius $12$ ft if the arc subtends a central angle of $135 ^ { \circ }$ .

Find the area of a sector with central angle $5 \pi / 4$ in a circle with radius $0.5$ m.

If $\sin \theta = \frac { \sqrt { 3 } } { 2 }$ for $\theta$ In quadrant I, find $\tan \theta + \sec \theta$

Find the measure of the central angle $\theta$ in a circle of radius 8 ft if the angle is subtended by an arc of length 7 ft.

Find $\sin \theta$ and $\cos \theta$ given that $\sec \theta = - 2$ and $\tan \theta > 0$ .

Rewrite the expression as an algebraic expression in x. $\sin \left( \cos ^ { - 1 } x \right)$

Find the reference angle for the given angles a) $- 202 ^ { \circ }$ b) $\frac { 19 \pi } { 6 }$

Rewrite the expression as an algebraic expression in x. $\sin \left( \cos ^ { - 1 } x \right)$

Land on a small Caribbean island is valued at $\$ 45$ per square foot. What is the value of a triangular lot with sides of lengths $80$ Ft, $50$ Ft, and $120$ Ft?

Solve the triangle. $a = 72.5 , \quad \angle B = 60 ^ { \circ } , \quad \angle C = 83 ^ { \circ }$

Find the indicated angle $\theta$ . $Find the indicated angle \theta .$

Sketch the triangle given by $\angle A = 23 ^ { \circ }$ , $\angle B = 78 ^ { \circ }$ , $c = 88$ , and solve it using the Law of Sines

A $95 - \mathrm { t }$ tree casts a shadow that is $45$ Ft long. What is the angle of elevation of the sun?

Find the exact value of the expression. $\csc \left( \cos ^ { - 1 } \frac { 24 } { 25 } \right)$