Deck 5: Analytic Trigonometry

Question 1

Determine whether the Law of Sines or the Law of Cosines is needed to solve the tri- angle. Then solve the triangle.

Answer 1

C

Question 2

Use the Heron's formula to find the area of the triangle. Round your answer upto two decimal places.

Answer 2

B

Question 3

Evaluate the expression.

Answer 3

B

Question 4

Use a calculator to calculate the value of from the given identity.

Question 5

Use the given values to evaluate (if possible) three trigonometric functions cosx, cscx, tanx.

Question 6

Use the trigonometric substitution to select the algebraic expression as a trigonomet-

A)
B)
C)
D)
E)

Question 7

Use the cofunction identities to evaluate the expression without using a calculator.

Question 8

Find the expression as the sine or cosine of an angle.

Question 9

Solve the following equation.

Question 10

Use the figure to find the exact value of the trigonometric function.

Question 11

Evaluate the following expression.

Question 12

A weight is attached to a spring suspended vertically from a ceiling. When a driving force is applied to the system, the weight moves vertically from its equilibrium position, and this
Motion is modeled by where is the distance from equilibrium (in feet) and is the time (in seconds). Use the identity

Question 13

Use the sum-to-product formulas to select the sum or difference as a product.

Question 14

Use a graphing utility to select the correct graph in the same viewing window. Use the graphs to determine whether . Explain your reasoning.

Question 15

Use the given values to evaluate (if possible) three trigonometric functions

Question 16

Use inverse functions where needed to find all solutions (if they exist) of the given equation on the interval .

Question 17

Use the law of Cosines to solve the given triangle. Round your answer to two decimal places.

Question 18

Use the Law of Sines to solve (if possible) for . Round your answers to two decimal places.

Question 19

Use the half-angle formulas to determine the exact value of the given trigonometric expression.

Question 20

Evaluate the following expression.

Question 21

Evaluate the expression.

Question 22

Use the given values to evaluate (if possible) three trigonometric functions cosx, cscx, tanx.

Question 23

Evaluate the following expression.

Question 24

Use a graphing utility to graph the function.

Question 25

Use the half-angle formulas to determine the exact value of the given trigonometric expression.

Question 26

Solve the following equation.

Question 27

A weight is attached to a spring suspended vertically from a ceiling. When a driving force is applied to the system, the weight moves vertically from its equilibrium position, and this
Motion is modeled by where is the distance from equilibrium (in feet) and is the time (in seconds).

Question 28

Find all solutions of the following equation in the interval

Question 29

Find the expression as the sine or cosine of an angle.

Question 30

Use the Law of Sines to solve (if possible) for . Round your answers to two decimal places.

Question 31

Use the figure to find the exact value of the trigonometric function.

Question 32

Use the cofunction identities to evaluate the expression without using a calculator.

Question 33

Use the sum-to-product formulas to select the sum or difference as a product.

Question 34

Given , use the Law of Cosines to solve the triangle for the value of C. Round answer to two decimal places.

A)
B)
C)
D)
E)

Question 35

Use the trigonometric substitution to select the algebraic expression as a trigonomet-

Question 36

Evaluate the following expression.

Question 37

Use a calculator to calculate the value of from the given identity.

Question 38

Use inverse functions where needed to find all solutions (if they exist) of the given equation on the interval

Question 39

Use a graphing utility to select the correct graph in the same viewing window. Use the graphs to determine whether Explain your reasoning.

Question 40

Use the given values to evaluate (if possible) three trigonometric functions cosec

Question 41

Given , use the Law of Cosines to solve the triangle for the value of C. Round answer to two decimal places.

Question 42

Evaluate the following expression.

Question 43

Use a double-angle formula to rewrite the expression.

Question 44

Evaluate the following expression.

Question 45

The monthly sales S (in hundreds of units) of baseball equipment for an Internet sporting goods site are approximated by

A) March through September
B) April through August
C) March through August
D) August through April
E) May through September

Question 46

Simplify the following expression algebraically.

Question 47

Use the Heron's formula to find the area of the triangle. Round your answer upto two decimal places.

Question 48

Determine whether the Law of Sines or the Law of Cosines is needed to solve the tri- angle. Then solve the triangle.

Question 49

Perform the multiplication and use the fundamental identities to simplify.

Question 50

Use the given values to evaluate (if possible) three trigonometric functions sinx, cosx, cotx.

Question 51

Use the formula where to find the trigonometric expression in the following forms.

Question 52

Simplify the expression algebraically.

Question 53

Use the trigonometric substitution to select the algebraic expression as a trigonomet- ric function of , where . Then find

Question 54

The table shows the average daily high temperatures in Houston H (in degrees Fahr- enheit) for month t, with corresponding to January. Select the correct scatter plot from the above data.

Question 55

Use the law of Cosines to solve the given triangle. Round your answer to two decimal places.

Question 56

Find all solutions of the following equation in the interval .

Question 57

Find the rate of change of the function

Question 58

Evaluate the expression.

Question 59

Use the sum-to-product formulas to select the sum or difference as a product.

Question 60

Solve the following equation.

Question 61

Use the low of Cosines to solve the given triangle. Round your answer to two decimal places.

Question 62

Find the area of the triangle having the indicated angle and sides. (Round your answer to one decimal place.)

Question 63

Find all solutions of the given equation in the interval

Question 64

Use the Law of Sines to solve (if possible) the triangle. Round your answers to two decimal places.

Question 65

Determine the angle in the design of the streetlight shown in the following figure.

Question 66

Determine whether the Law of Sines or the Law of Cosines is needed to solve the tri- angle. Then solve the triangle. Round your answer to two decimal places.

Question 67

Given , use the Law of Cosines to solve the triangle for the value of B. Round answer to two decimal places.