Question 1

A $75$ ft tree casts a shadow that is $45$ ft long. What is the angle of elevation of the sun?

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Question 2

Find the exact value of $\cot \left( - 675 ^ { \circ } \right)$ .

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Question 3

Find the radian measures that correspond to the degree measures $- 1080 ^ { \circ }$ and $15 ^ { \circ }$ .

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Question 4

Use the Law of Sines to solve for all possible triangles that satisfy $b = 13$ , $c = 17$ , $\angle B = 43 ^ { \circ }$ .

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Question 5

Solve the triangle. $\angle C = 52 ^ { \circ }$ , $a = 1.54$ , $b = 1.87$

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Question 6

A boy is riding a scooter whose wheels are $5$ inches in diameter. If the wheels rotate at $550$ rpm, find the speed at which he is traveling in mi/h.

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Question 7

Two tugboats are pulling a barge with cables $50$ m and $62$ m long. If the angle between the cables is $33 ^ { \circ }$ approximately how far apart are the barges?

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Question 8

Solve the triangle. $\angle A = 53 ^ { \circ }$ , $b = 11$ , $c = 23$

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Question 9

Solve the triangle using the Law of Sines.

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Question 10

Solve for $x$ correct to one decimal place.

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Question 11

Use the Law of Sines to solve for all possible triangles that satisfy $\angle A = 25 ^ { \circ }$ , $a = 5$ , $b = 8$ .

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Question 12

Find the length of an arc of a circle of radius $3$ m if the arc subtends a central angle of $75 ^ { \circ }$ .

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Question 13

Two cities, $A$ and $B$ lie on the same meridian, one is found at $20 ^ { \circ }$ S and the other at $27 ^ { \circ }$ S. Find the distance between these cities given that the circumference of the earth is $3960$ mi.

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Question 14

Find the exact value of the expression. $\tan \left( \cos ^ { - 1 } \frac { 5 } { 13 } \right)$

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Question 15

Sketch the triangle given by $\angle A = 113 ^ { \circ }$ , $\angle B = 37 ^ { \circ }$ , $c = 25$ , and solve it using the Law of Sines.

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Question 16

Find the exact value of $\cot ( 18 \pi / 4 )$ .

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Question 17

Find the exact value of $\csc ( - \pi / 3 )$ .

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Question 18

Find the angle $\theta$ in the triangle.

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...

Question 19

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

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Exam 6: Trigonometric Functions: Right Triangle Approach

A $75$ ft tree casts a shadow that is $45$ ft long. What is the angle of elevation of the sun?

Find the exact value of $\cot \left( - 675 ^ { \circ } \right)$ .

Find the radian measures that correspond to the degree measures $- 1080 ^ { \circ }$ and $15 ^ { \circ }$ .

Use the Law of Sines to solve for all possible triangles that satisfy $b = 13$ , $c = 17$ , $\angle B = 43 ^ { \circ }$ .

Solve the triangle. $\angle C = 52 ^ { \circ }$ , $a = 1.54$ , $b = 1.87$

A boy is riding a scooter whose wheels are $5$ inches in diameter. If the wheels rotate at $550$ rpm, find the speed at which he is traveling in mi/h.

Two tugboats are pulling a barge with cables $50$ m and $62$ m long. If the angle between the cables is $33 ^ { \circ }$ approximately how far apart are the barges?

Solve the triangle. $\angle A = 53 ^ { \circ }$ , $b = 11$ , $c = 23$

Solve the triangle using the Law of Sines.

Solve for $x$ correct to one decimal place.

Use the Law of Sines to solve for all possible triangles that satisfy $\angle A = 25 ^ { \circ }$ , $a = 5$ , $b = 8$ .

Find the length of an arc of a circle of radius $3$ m if the arc subtends a central angle of $75 ^ { \circ }$ .

Two cities, $A$ and $B$ lie on the same meridian, one is found at $20 ^ { \circ }$ S and the other at $27 ^ { \circ }$ S. Find the distance between these cities given that the circumference of the earth is $3960$ mi.

Find the exact value of the expression. $\tan \left( \cos ^ { - 1 } \frac { 5 } { 13 } \right)$

Sketch the triangle given by $\angle A = 113 ^ { \circ }$ , $\angle B = 37 ^ { \circ }$ , $c = 25$ , and solve it using the Law of Sines.

Find the exact value of $\cot ( 18 \pi / 4 )$ .

Find the exact value of $\csc ( - \pi / 3 )$ .

Find the angle $\theta$ in the triangle. $Find the angle \theta in the triangle.$

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

Exam 6: Trigonometric Functions: Right Triangle Approach

A 757575 ft tree casts a shadow that is 454545 ft long. What is the angle of elevation of the sun?

Find the exact value of cot⁡(−675∘)\cot \left( - 675 ^ { \circ } \right)cot(−675∘) .

Find the radian measures that correspond to the degree measures −1080∘- 1080 ^ { \circ }−1080∘ and 15∘15 ^ { \circ }15∘ .

Use the Law of Sines to solve for all possible triangles that satisfy b=13b = 13b=13 , c=17c = 17c=17 , ∠B=43∘\angle B = 43 ^ { \circ }∠B=43∘ .

Solve the triangle. ∠C=52∘\angle C = 52 ^ { \circ }∠C=52∘ , a=1.54a = 1.54a=1.54 , b=1.87b = 1.87b=1.87

A boy is riding a scooter whose wheels are 555 inches in diameter. If the wheels rotate at 550550550 rpm, find the speed at which he is traveling in mi/h.

Two tugboats are pulling a barge with cables 505050 m and 626262 m long. If the angle between the cables is 33∘33 ^ { \circ }33∘ approximately how far apart are the barges?

Solve the triangle. ∠A=53∘\angle A = 53 ^ { \circ }∠A=53∘ , b=11b = 11b=11 , c=23c = 23c=23

Solve the triangle using the Law of Sines.

Solve for xxx correct to one decimal place.

Use the Law of Sines to solve for all possible triangles that satisfy ∠A=25∘\angle A = 25 ^ { \circ }∠A=25∘ , a=5a = 5a=5 , b=8b = 8b=8 .

Find the length of an arc of a circle of radius 333 m if the arc subtends a central angle of 75∘75 ^ { \circ }75∘ .

Two cities, AAA and BBB lie on the same meridian, one is found at 20∘20 ^ { \circ }20∘ S and the other at 27∘27 ^ { \circ }27∘ S. Find the distance between these cities given that the circumference of the earth is 396039603960 mi.

Find the exact value of the expression. tan⁡(cos⁡−1513)\tan \left( \cos ^ { - 1 } \frac { 5 } { 13 } \right)tan(cos−1135​)

Sketch the triangle given by ∠A=113∘\angle A = 113 ^ { \circ }∠A=113∘ , ∠B=37∘\angle B = 37 ^ { \circ }∠B=37∘ , c=25c = 25c=25 , and solve it using the Law of Sines.

Find the exact value of cot⁡(18π/4)\cot ( 18 \pi / 4 )cot(18π/4) .

Find the exact value of csc⁡(−π/3)\csc ( - \pi / 3 )csc(−π/3) .

Find the angle θ\thetaθ in the triangle.

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

A $75$ ft tree casts a shadow that is $45$ ft long. What is the angle of elevation of the sun?

Find the exact value of $\cot \left( - 675 ^ { \circ } \right)$ .

Find the radian measures that correspond to the degree measures $- 1080 ^ { \circ }$ and $15 ^ { \circ }$ .

Use the Law of Sines to solve for all possible triangles that satisfy $b = 13$ , $c = 17$ , $\angle B = 43 ^ { \circ }$ .

Solve the triangle. $\angle C = 52 ^ { \circ }$ , $a = 1.54$ , $b = 1.87$

A boy is riding a scooter whose wheels are $5$ inches in diameter. If the wheels rotate at $550$ rpm, find the speed at which he is traveling in mi/h.

Two tugboats are pulling a barge with cables $50$ m and $62$ m long. If the angle between the cables is $33 ^ { \circ }$ approximately how far apart are the barges?

Solve the triangle. $\angle A = 53 ^ { \circ }$ , $b = 11$ , $c = 23$

Solve for $x$ correct to one decimal place.

Use the Law of Sines to solve for all possible triangles that satisfy $\angle A = 25 ^ { \circ }$ , $a = 5$ , $b = 8$ .

Find the length of an arc of a circle of radius $3$ m if the arc subtends a central angle of $75 ^ { \circ }$ .

Two cities, $A$ and $B$ lie on the same meridian, one is found at $20 ^ { \circ }$ S and the other at $27 ^ { \circ }$ S. Find the distance between these cities given that the circumference of the earth is $3960$ mi.

Find the exact value of the expression. $\tan \left( \cos ^ { - 1 } \frac { 5 } { 13 } \right)$

Sketch the triangle given by $\angle A = 113 ^ { \circ }$ , $\angle B = 37 ^ { \circ }$ , $c = 25$ , and solve it using the Law of Sines.

Find the exact value of $\cot ( 18 \pi / 4 )$ .

Find the exact value of $\csc ( - \pi / 3 )$ .

Find the angle $\theta$ in the triangle. $Find the angle \theta in the triangle.$

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