Trigonometry Questions and Answers

13 Dimensions of a Mirror A person standing 150 centimeters from a mirror notices that the angle of depression from his eyes to the bottom of the mirror is 12 while the angle of elevation to the top of the mirror is 11 Find the vertical dimension of the mirror See Figure 16 150 cm

PART A 1 2 3 4 5 6 7 9 10 11 12 MULTIPLE CHOICE What is the radius of a circle with the equation of x2 y 64 a 8 b 16 c 25 d 64 What is the length of the line segment joining A 4 7 and B 16 9 a 13 4 b 180 c 656 d 25 6 What is the optimal value of this quadratic function a 2 b 1 C 2 d 1 What is the greatest common factor for 24m n4 4m n 16m n a 4 b 4m n c 48m n4 d 4mn What is the expression 2x 5 in expanded simplified form a 4x 10x 25 b 4x 20x 25 c 4x 5 What is the vertex of the quadratic relation y 5 x 1 8 a 1 8 b 1 8 c 1 8 d 1 8 e x 1 What are the roots of the quadratic relation y x 5x 14 a x 0 x 24 b x 2 x 7 d x 2 x 7 e x 2 x 7 For the quadratic relation y x 3x 2 what is the y intercept a 1 b 3 c 2 d 0 e 1 and 2 Use the following triangle to answer questions 9 12 D 12cm Sin F is 5 13 a E 5 cm F Cos F is 5 13 a Tan D is a 13 cm 13 b 1 2 5 12 5 12 The degree of LF is a 0 385 b 0 923 12 13 12 c 13 c 12 13 c 2 4 d 2 2 d 1 3 d 1 3 5 d 22 6 e 1322 e c x 5 x 14 13 12 13 e 122 e 67 4 e 128W e 12 e 4m n d 4x 25 1

3 a Dilation of about point M 7 5 M N M 9 8 7 5 N Center to M N 9 8 6 y Center to P O Center to P O Center to 4 a Dilation of about the point 6 5 3 X Y Center to 1 8 3 0 7 Z X Y 771 Center to

A 12m tall flagpole was installed in the park A long cable is tied to the top and secured to the ground The angle the cable makes with the ground is 65 It was unsafe so they had to move it further away so it makes an angle of 50 with the ground How much further away was the cable secured to the ground Provide a detailed diagram with your solution round to one decimal A 5 marks place

Vome Alice At the local garden shop a package of flower seeds costs 5 and trees costs 17 The gardener purchased 500 items and the total cost is 5 968 a Model this situation using a system of equations 4 b How many trees did the gardener purchase 5 C 3 marks K 3 marks The city wants to build a stage in the park The stage needs a ramp The rules say that the angle of elevation for the ramp must be 8 or less and the ramp must be 15m or less in length With these rules what would be the maximum height for the stage Round to I decimal place Provide a detailed diagram T 4 marks

sin 0 11 cos 0 tan 8 csc 8 sec 0 cot 0 values of the six trigonometric functions of the angle 8 shown in the figure 12 13 13 S X X x X 12

A buoy floating in the ocean is bobbing in simple harmonic motion with period 8 seconds and amplitude 4 ft Its displacement from sea level at time t 0 seconds is 0 ft and initially it moves downward Note that downward is the negative direction Give the equation modeling the displacement d as a function of time t d 0 T sin cos

Match each angle in Column I with its reference angle in Column II 45 37 31 83 60 30 Drag each reference angle above to the corresponding angle below Answers 97 211 150 45 780 495

The angle of elevation from a point on the ground to the top of a pyramid is 40 40 The angle of elevation from a point 164 feet farther back to the top of the pyramid is 14 30 Find the height of the pyramid What is the height of the pyramid ft Round to the nearest integer 14 30 164 40 40

12 5 m fire truck ladder is leaning against a wall Find the distance d the ladder oes up the wall above the fire truck if the ladder makes an angle of 27 21 with ne horizontal 12 5 m 27 211 COB Simplify your answer Type an integer or a decimal Round to the nearest hundredth

Coast Guard Station Able is located L 250 miles due south of Station Baker A ship at sea sends an SOS call that is received by each station The call to Station Able indicates that the ship is located N55 E the call to Station Baker indicates that the ship is located S60 E Use this information to answer the questions below a How far is each station from the ship The distance from Station Able to the ship is miles Do not round until the final answer Then round to two decimal places as needed

Now that you are familiar with the way a demand curve is graphed you will create your own graph to submit to your instructor Step 1 Launch the data generator to get started Print or copy the data table to use in the next step Step 2 Create a demand graph Correctly label the x axis and y axis with the terms price and quantity Assign values for price and quantity along each axis Consider the numbers in your data table and the size of your graph For example you may want to label in increments of 25 Create a title for your graph by choosing a good or service for the data to represent Using the data table from Step 1 plot a demand curve and label the curve D Step 3 Add a curve to your graph that represents an increase in demand Label the new curve D1 Step 4 In a few sentences explain a situation that could have resulted in the demand increase Be sure to Make your situation specific to the product or service you chose in Step 2 Use at least one factor from the acronym TRIBE in your explanation Step 5 Add another curve to your graph that represents a decrease in demand Label the new curve D2 Step 6 In a few sentences explain a situation that could have resulted in the demand decrease Be sure to Make your situation specific to the product or service you chose in Step 2 Use at least one factor from the acronym TRIBE in your explanation

sin t cos t tan t 3 CSC t sec t cot t

S 7 An airplane is heading due west at 400 km h when it encounters a wind from the northeast at 120 km h Using Cartesian Vectors components determine how far the airplane will travel in three hours Round to the nearest kilometre

E it uzunluktaki kenarlar ndan biri 1 birim olan renkleri d nda e ikizkenar 9 gen ekildeki gibi birle tirilerek dokuzgen olu turmu tur Buna g re genlerden birinin taban uzunlu u a a dakilerden hangisine e ittir A 2 cos 20 B 2 sin 20 D cosec 20 2 E C 2 sec 20 sec 20 2

Two dice are rolled Find the odds in favor of rolling the following a A sum of 5 b A sum of 7 or 12 c A sum less than 8 d Not a sum of 7

2 7 pts Solve the triangle if A 35 C 66 and b 11 Round to two decimal places if needed Assume A is the angle opposite side a B is the angle opposite side b and Cis the angle opposite side c You must draw the triangle to get credit for this problem

A wall that is 2 3 meters high casts a shadow that is 3 7 meters long A pole located beside the wall casts a shadow that is 10 2 meters long Find the height of the pole rounded to the nearest 0 1 meters A 6 3 meters B 8 8 meters C 11 6 meters D 16 4 meters E None of these

7 Using the grid provided sketch the graph of the given function in the interval 5 5 and then determine the x intercepts if any TCX 1

Question 2 A B Y Using a double angle or half angle formula to simplify the given expressions a If cos 27 sin 27 cos 4 then degrees b If cos 7x sin 7x cos B then

Question 11 Find the exact value of cos 75 Question Help Video 1 Video 2

Question 9 Determine the value of sin x cos x for x Question Help Video Submit O ion 20 degrees

Question 8 Simplify and write the trigonometric expression in terms of sine and cosine tan x sec x Question Help Worked Example 1 LI

Question 5 Simplify 1 sin t sin t to an expression involving a single trig function with no fractions If needed enter squared trigonometric expressions using the following notation Example Enter sin t as sin t 0 10

A video game is programmed using vectors to represent the motion of ob jects The programmer is programming a human character s path to an object The object is 30 meters to the right 20 meters in front of the human character Part One Write a vector to represent the path to the object Part Two How far is the object from the human character Part Three A second human character is 40 meters to the left of the first human character and is 50 meters ahead of the first human character The first human character is currently facing the previously mentioned object If the programmer wants to rotate the first human in order to make it face the second human what angle of rotation is needed Hint You could create a vector between the first and second human then calculate the angle between the first and second vectors

Find a function of the form y A sin kx C or y A cos kx C whose graph matches this one 16 15 14 13 12 11 10 9 8 7 6 5 6 4 3 A 3 2 2 3 2 3 4 5 y Leave your answer in exact form if necessary type pi for 6 7 8 9 10 11 12

0 10 pts 399 Details 1 5 4 3 2 1 1 N 2 3 Amplitude 2 Period Midline y 5 Based on the graph above determine the amplitude midline and period of the function 6 1 2 3 4 5

0 10 pts 399 Details Given the equation y 2 sin 6x 18 8 The amplitude is The period is The horizontal shift is units to the Select an answer The midl

For the proprablility distribution table below x x l 0 1 2 3 4 P x 0 1 0 18 0 12 0 14 0 46 0000 Find the mean Round to two decimal places Find the standard deviation Round to three decimal places xP x 00000 x P x 00000

16 y sin x 5 cos x

Question 3 of 20 This test 65 point s possible This question 4 point s possible Solve the following trignometric equation analytically and by use of a graphing calculator Compare the results Use values of x for 0 x 2x 12 sin 2x cos x sin x 0 GELEE Type an exact answer using x as needed Use a comma to separate answers as needed Use integers or fractions for any numbers in the expression Simplify your ans

5 Suppose sin x and 270 x 360 a 5 pts Use identities to find the exact value of sin b 5 pts Use identities to find the exact value of cos c 5 pts In what quadrant is the angle Explain your answer

Suppose cos x and 90 x 180 a 5 pts Use identities to find the exact value of sin 2x b 5 pts Use identities to find the exact value of cos 2x c 5 pts In what quadrant is the angle 2x Explain your answer

2 10 pts Solve the following triangle that is find A B and c Don t forget to show your work Round your answers to one decimal place B a 14 25 C b 7 PADLESEX LLEGE

tlook 42 K D2 Homepage 23F Technology Mathemati Prove the given identity tan x sec x csc x cot x Choose the correct proof below O A tan x sec xcsc x sin x cos x sin x cos x 2 1 sin x sin x cos x cot x cos x OC tan x sec xcsc x sin x the C COS X 1 sin x 2 sin x cos x cos x sin x cos x cot x mylab pearson com Pearson MyLab and Mastering Question 7 of 10 OB tan x sec xcsc x sin x 1 1 cos x cos x sin x 1 sin x cot x are b Dat sin x cos x cos x sin x cos x P In class Quiz 2 2 1 sinx sin x cos x COS X This quiz 25 point s pos This question 3 point s OD tan x sec xcsc x sin x 1 1 cOS X sin x cos x cot x cos x sin x

Verify the following identity sin 2x 1 cos2x tan x O Which of the following three statements verifies the given equation O 2 T C sin 2x 1 cos2x sin 2x 1 cos2x sin 24 L nical 1 2 cos x 1 2 sinx cos x 1 2 sin x 1 2 cos2x 2 sinx cos x 2 sin x ng Ques 51

Find the exact value of 1 2 sin x cos x 2 sin x cos 2x Question 9 a 1 2 sin x cos x 2 sin 4x cos 2x Simplify your answer

Prove the given identity sec x csc X sin x sec x cos XCSC X Choose the correct proof below OA sec xcsc x sin xsec x 1 cos x sin x 2 1 sinx sin x cos x COS2 X sin x cos x cos X CSC X OC sec xcsc x sin xsec x 1 COS X sin x sin x cos x 2 1 sin x sin x cos x 2 COS X cos X CSC X Question 10 of 10 OB sec xcsc x sin xsec x 1 sin x cos X sin x sin X This quiz 25 This question sin x cos x 2 COS X sin x cos x cos XCSC X OD sec xcsc x sin xsec x 1 COS X sin x sin x cos x 1 sin X sin x cos x 2 COS X cos X CSC X 1 sin x cos 1 cos x

3 Find the length of segment Hint There is a right angle and Pythagorean Thm will be necessary a d 68 a 42 11 d b e e C 15 b 17 C 4 Find the measure of each angle a d a4 C d 75 b b e 10 cm 49 6 cin e 14 cm C

A hot air balloon is floating above a straight road To calculate their height above the ground the balloonists simultaneously measure the angle of depression to two consecutive mileposts on the road on the same side of the balloon The angles of depression are found to be 14 and 18 How high in feet is the ballon

Solve the triangle ABC if the triangle exists B 35 12 a 39 7 b 28 8 OA There is only 1 possible solution for the triangle The measurements for the remaining angles A and C and side c are as follows 0 mZA The length of side c 0 mZC Simplify your answer Round to the nearest degree as needed Round to the nearest minute as needed OB There are 2 possible solutions for the triangle Round to the nearest tenth as needed The measurements for the solution with the longer side c are as follows mZA mZC The length of side c Simplify your answer Round to the nearest degree as needed Round to the nearest minute as needed The measurements for the solution with the shorter m A O 0 mZC Simplify your answer Round to the nearest degree as needed Round to the nearest minute as needed OC There are no possible solutions for this triangle Round to the nearest tenth as needed side care as follows The length of side c Round to the nearest tenth as needed

solve a triangle SSS Click here to watch the video Solve the triangle if possible IRERI A 0 12 0 19 Find the measure of angle A Select the correct choice below and if necessary fill in the answer box to complete your choice 10 A A 27 36 Do not round until the final answer Then round to two decimal places as needed B There is no solution AB OA B Do not round until the final answer Then round to two decimal places as needed OB There is no solution Find the measure of angle B Select the correct choice below and if necessary fill in the answer box to complete your choice

3 8 Let z x20 y10 dz where x e5t and y sin 2t Use the Chain Rule to find dt when t k TU

Assume two satellites A B are in the same orbital plane Compute the in plane satellite positions XA YA for A and XB YB for satellite B given rA is 26 705 km and re is 27 512 km and the true anomaly fA 22 8 and B fB 95 3 respectively Compute the coordinate XA O 50987 651 km 5132 254 km 24618 355 km

tan 0 sin 0 sec 0 cos 0 Choose the correct proof below A B OC D tan 8 sin 0 sec 0 tan 0 sin 0 sec 0 tan 0 sin 0 sec 0 tan 0 sin 0 sec 0 sin 8 cos 0 sin 0 cos e sin 0 cos 8 sin e cos e 1 cos e sin 8 sec 0 sin 0 sin 8 sin 0 1 cos e 1 Cos 0 cos e sin 0 1 cos 0 cos sin 0 1 2 sin 0 1 cos e sin 0 1 cos 0 cos e s 0 cos cos e cos 0 cos 0 cos e cos cos 0 cos 0 cos 0 cos 0 cos 0

sin 20 Which of the following four statements establishes the identity 2 cot 0 2 cot 0 1 cot 0 2 cot 0 1 cot 0 2 2 O A sin 20 sin 0 cos 0 OB sin 20 2 cos 0 sin 0 O C sin 202 cos 0 sin 0 sec 0 2 2 cot 0 O D sin 20 sin 0 cos 0 CSC 2 0 2 cot 0 sec 0 2 2 cot 0 csc 0 2 cot 0 1 cot 0 2 cot 0 1 cot 0 2 cot 0 1 cot 0

Simplify the given expression The result will be one of sinx cos x tan x cotx sec x or csc x cos x sec x cot x cos x sec x cot x

16 sin 6x cos 6x 16 sin 6x cos 6x

A carpet is to be installed in one room and a hallway as shown in the diagram below At a cost of 14 50 per square meter how much will it cost to carpet the area Assume a 4 7 m b 6 5 m and c 10 7 m Round your answer to the nearest cent 1173 38 X

llar course shown in the figure below C 433 mi 300 mi 200 mi B A a Use the Law of Cosines to find the angle located at vertex B Round to the nearest degree as needed b Use the Law of Sines to find the angle a located at vertex A Round to the nearest degree as needed