Deck 5: Analytic Trigonometry

Question 1

Use a power-reduction formula to find the exact value (Hint: What is =?)

Answer 1

Question 2

For positive values of a,c and γ where
and c

A) one unique triangle
B) two triangles are possible
C) no triangles are possible
D) more information is necessary to decide.

Answer 2

no triangles are possible

Question 3

Use the grapher to determine which of the following is an identity.

A)
B)
C)
D)
E)

Answer 3

Question 4

The angle of elevation to the bottom of a steeple of a church is and the angle of elevation to the top of the steeple is https://d2lvgg3v3hfg70.cloudfront.net/TB34225555/. If the angles of elevation are measured from a point on the ground 60 meters from the church steeple, what is the height of the steeple?

Question 5

Factor the expression and use fundamental identities to simplify.

Question 6

Prove the identity:

Question 7

What is the area of if a=8, b=10 , and c=15 ?

Question 8

Which of the following is correct?

A)
B)
C)
D)
E)

Question 9

Confirm or disprove the following: 2 cos x=sin 2 x . If this is an identity, provide a confirmation. If it is not an identity, provide a counter example.

Question 10

Which of the following is not a valid completion of the double-angle identity for

A)
B)
C)
D)

Question 11

Find all solutions of the equation on the interval (Your answer should be exact.)

Question 12

Prove the identity:

Question 13

A civil engineer needs to measure the length of a proposed tunnel through a mountain. The engineer chooses a point that can be seen from each end of the tunnel and measures the distance to each end of the tunnel to be 3,000 meters and 4,200 meters, respectively. If the angle between the two distances is what is the length of the tunnel?

Question 14

Simplify the expression

Question 15

Solve the equation
by factoring and/or extracting square roots.

Question 16

What is the area of if b=17 , and c=25 ?

Question 17

Use the sum identities to prove the identity:

Question 18

Two points are 200 ft apart on opposite sides of a tree. The angles of elevation from each point to the top of the tree are and What is the height of the tree?

Question 19

Solve the inequality

Question 20

In triangle ABC, and b=6. Find the remaining sides and angle.

Question 21

The angles of elevation to the top of a tower from two points that are on the same side of the tower and 30 meters apart are
What is the height of the tower?

Question 22

Prove the identity:

Question 23

Use a grapher to conjecture whether the equation is likely to be an identity. If it is not, give a counter example.

Question 24

Prove the identity:

Question 25

Due to the wind, a tree grew so that it leaned from the vertical. From a point on the ground 28 meters from the base of the tree, the angle of elevation to the top of the tree is What is the height of the tree?

Question 26

Use the fundamental identities to change the expression to one involving only sines and cosines. Then simplify. Show all your steps.

Question 27

Use a grapher to conjecture whether the equation is likely to be an identity. If it is not, give a counter example.

Question 28

If a=9, b=8 , and

Question 29

A golf ball is hit with initial velocity (in feet per second) and trajectory angle The horizontal distance traveled before it bounces is given by
Find the angle of trajectory needed to hit a green 700 feet away on the first bounce if the initial velocity is 170 ft/sec.

Question 30

Use the half-angle identities to express sin 3 C in terms of a function of 6C .
In Problems 8-9, consider the triangle ABC . Express your answers as decimals rounded to the nearest hundredth. If more than one triangle is possible, give all possible answers.

Question 31

What is the general solution to

Question 32

Suppose the angle is formed by two sides of length 8 in an isosceles triangle. Find an expression for the area of the triangle. Then find the value(s) of so that the triangle's area is 25 .

Question 33

Use a sum or difference identity to find the exact value of sin

Question 34

Kelly must find the distance between points A and C on opposite sides of a lake. She locates a point B that is 425 ft from A and 672 ft from C . If the angle at B is what is the distance AC ?

Question 35

Use a sum or difference identity to find the exact value of cos

Question 36

What is the general solution to

Question 37

Use the fundamental identities to change the expression to one involving only sines and cosines. Then simplify. Show all your steps.

Question 38

Prove the identity:

Question 39

The lengths of the sides of a triangular parcel of land are 300 ft, 350 ft , and 450 ft . What is the area, in square feet, of the parcel of land?

Question 40

If a=8, b=10 , and how many triangles are determined?

Question 41

Randy must find the distance between points B and C on opposite sides of a lake. He locates a point A that is 385ft from B and 546 ft from C . If the angle at A is what is the distance BC ?

Question 42

If a=10, b=8 , and how many triangles are determined?

Question 43

The angles of elevation to the top of a tower from two points that are on the same side of the tower and 30 meters apart are and What is the height of the tower?

Question 44

The lengths of the sides of a triangular parcel of land are 200 ft, 250 ft , and 350 ft . What is the area, in square feet, of the parcel of land?

Question 45

Due to the wind, a tree grew so that it leaned from the vertical. From a point on the ground 30 meters from the base of the tree, the angle of elevation to the top of the tree is What is the height of the tree?

Question 46

A golf ball is hit with initial velocity (in feet per second) and trajectory angle The horizontal distance traveled before it bounces is given by
Find the angle of trajectory needed to hit a green 800 feet away on the first bounce if the initial velocity is 200 ft/sec

Question 47

Suppose the angle is formed by two sides of length 10 in an isosceles triangle. Find an expression for the area of the triangle. Then find the value(s) of so that the triangle's area is 37 .

Question 48

Use the half-angle identities to express cos 4C in terms of a function of 8C .
In Problems 8-9, consider the triangle ABC . Express your answers as decimals rounded to the nearest hundredth. If more than one triangle is possible, give all possible answers.

Question 49

Prove the identity:

Question 50

If a=9, b=8 , and