Trigonometry Questions and Answers

19 Distance between Two Docks Two docks are located on an east west line 2587 ft apart From dock A the bearing of a coral reef is 58 22 From dock B the bearing of the coral reef is 328 22 Find the distance from dock A to the coral reef

The vice president of operations at Busch Gardens knows that 70 percent of the patrons like roller coaster rides Therefore he wishes to have an acceptable margin of error of no more than 3 percent and wants to be 95 percent confident about the attitudes toward the Gwazi roller coaster What sample size would be required for a personal interview study among on site patrons SHOW YOUR WORK FOR CREDIT

Given s t 1 4t where s t is in feet and t is in seconds find each of the following a v t b a t c The velocity and acceleration when t 2 sec a v t 2t 4 b a t

Solve the given initial value problem x y 2x 1 y 1 5 dy dx y x Give the largest interval I over which the solution is defined Enter your answer using interval notatie I

As you inflate a spherical balloon its radius increases by 5 mm per second The function r t 5t gives the balloon s radius r in mm after t seconds The 4 3 volume V of a sphere is given by V r r where r is the sphere s radius Write a function that gives the balloon s volume after t seconds

a For the scalar field f x y x y calculate the line integral of the function Vf from point 0 0 0 to point P ro yo along the paths C C2 and C3 as shown in the figure Verify the fundamental theorem of gradients 6 A 0 0 0 G P x y 8 b Writing Vf V verify whether V is an irrotational vector or not Can you make a comment on the integral fe V dl where C OAPBO without doing the integral explicitly

A dam is 10 m high and 20 m wide but with a triangular cross section as shown in the figure The angle 0 60 If the body of water behind the dam is 9 m deep h in the figure what is the net vertical component of pressure force acting on the face of the dam rounded to the nearest kN fill in blank 0 Fp P AV h

position Let s do a quick check how many different sections and in what ranges of x would be needed to obtain functions for internal loads in the structure shown below Please provide your answer in PlayPosit 2m 445 IKN 12m ZkN m bbbbb 2m 1 5KN A 2m lim 1m 3 KN A It needs 4 sections 0 to 2 2 to 5 5 to 8 and 8 to 10 B It needs 5 sections 0 to 2 2 to 4 4 to 6 6 to 8 and 8 to 10 C It It needs 6 sections 0 to 2 2 to 4 4 to 5 5 pause it and 8 to 10

A boat sailed from Kingston Harbour on a bearing of 060 to Port Q a distance of 500km The boat then sailed easterly to Port R a distance of 800km from Port Q 1 iii Sketch a clearly labelled diagram to illustrate the journey of the boat from Kingston to Port R Determine the distance between Kingston and Port R Calculate the area of the region bounded by the Kingston Harbor Port Q and Port R

3 in 2 in Find the volume and surface area of the right circular cylinder Volume in Use 3 14 for T Round to the nearest tenth Surface area in Use 3 14 for T Round to the nearest tenth

9 11 9 cm A 2 25 to 12 2 cm 12 cm

A boat heading out to sea starts out at Point A at a horizontal distance of 1433 feet from a lighthouse the shore From that point the boat s crew measures the angle of elevation to the lighthouse s beacon light from that point to be 15 At some later time the crew measures the angle of elevation from point B to be 6 Find the distance from point A to point B Round your answer to the nearest tenth of a foot if necessary

6 An airplane is flying on a bearing of N 30 W at 300 mph A strong jet stream speed wind of 90 mph is blowing at S 40 W a Find the vector representation of the plane an the wind b Find the resultant vector a b in component form that represents the actual course of the plane b Give the resulting speed and bearing of the plane N

Analysis To the right is a graph showing sin 0 versus sin 02 for your data 1 Use a curve fit to help determine a value for the index of refraction for the acrylic lens n Assume that the index of refraction for air n is 1 Record your experimental value here 2 If acrylic glass has a theoretical index of refraction of 1 49 what is the percent error on your experimental value 2 0 error Theoretical Experimental Theoretical 100 3 What caused error in your measurements and how could these have been avoided sin 0 1 0 0 9 0 8 0 7 0 6 0 5 0 4 0 3 0 2 0 1 0 0 00 01 02 03 Linear mx b m 1 47 0 0039 b 8 23x10 4 0 0017 r 1 000 04 05 06

Problem 6 Solve the linear programming problem You may find it useful to use desmos com to graph the constraints Maximize P 3x 2y subject to 2x y 20 2x 3y 24 The maximum is P at x and y y 6 x 0 y 0

A ranger in tower A spots a fire at a direction of 338 A ranger in tower B located 40 mi at a direction of 46 from tower A spots the fire at a direction of 294 How far from tower A is the fire How far from tower B The fire is from tower A Round to the nearest whole number 338 N A 46 40 mi N I B 294

A boat on the ocean is 2 mi from the nearest point on a straight shoreline that point is 12 mi from a restaurant on the shore A woman plans to row the boat straight to a point on the shore and then walk along the shore to the restaurant Complete parts a and b below 2 mi 12 mi a If she walks at 3 mi hr and rows at 2 mi hr at which point on the shore should she land to minimize the total travel time To minimize the total travel time the boat should land restaurant Type an exact answer using radicals as needed miles from the

Problem 4 Two fire towers Gold Tower and Tower B are 70 miles apart with Tower B due east of Gold Tower A fire is spotted from the towers Gold Towe eports the fire at a bearing of N 70 E and Tower B reports the fire at a bearing of N 60 W How far is the fire from Gold Tower How far is the fire from Tower B

The propeller of a small plane at full speed rotates exactly 7500 revolutions per min Find the angular speed of the propeller in degrees per second

3 If mA 20 1 a 14 9 ft and b 29 8 ft there are two possible solutions to the triangle Find both solutions m B m C C m B in

Listen A tree casts a shadow 8 feet long At the same time a person who is 5 feet tall casts a shadow that is 2 feet long How tall is the tree 1 20 feet 2 11 feet 3 17 feet 4 3 2 feet

urveyor standing on a hill 27 feet high looks at a building across a river The surveyor determines that the angle of depression to the base of the building is 26 9 and the angle of elevation to top of the building to be 32 26 Calculate the height of the building in feet to two decimal places feet 30 76 ihmit Apower Incorrect Trios 1 00 Drevious Tric

9 A flagpole sits on top of a tall building From the top of a smaller building the angle of elevation to the bottom of the flagpole is 34 shown while the angle of elevation to the top of the flagpole is 42 not shown The distances from the top of the smaller building to the bottom and top of the flagpole are 44 6 m and 49 8 m respectively shown How tall is the flagpole 5 marks I 34 49 8 m 42 44 6 m

h k K Given the figure above if 3 4 DJ 28 and j 3 2 use the sine law to determine DL to the nearest degree a 26 Ob 27 O c 60 L d 30

Given sin 0 2 5 of cos cos 0 B TU and B T 2 and cos where 3 2 3 4 determine the value

5 Consider the function y sin x 30 3 a Sketch the graph for two cycles 50 100 b What is the amplitude C What is the period e 150 200 d What is the equation of the axis State the domain and range 250 300 350 400 450 500 550 3 marks 600 650 1 mark 1 mark 1 mark 2 marks

in 2N cos 2N sin 2N 4 sin N cos N GLITR To verify the identity rewrite the more complicated side of the equation so that it is identical to the simpler side Choose the correct transformations and transform the expression at each sin 2N 4 sin Ncos N Use a double angle identity Use a reciprocal identity Combine like terms

In the diagram below angle A is in standard position Find the coordinates of point B and then find sin A cos A and tan A XB YB sin A COS A tan A

5 Determine an exact value for the expression APP TL I a cosesc sin 3

4 Find the exact value using CAST and drawing the special triangles for the following angle APP a cos 5 4

3 Determine the exact measures for each K a 75 in radians b 2 in degrees

One side of a triangle is increasing at a rate of 4 cm s and a second side is decreasing at a rate of 2 cays If the area of the triangle remains constant at what rate does the angle between the sid change when the first side is 28 cm long the second side is 34 cm and the angle is a 47 Round your answer to three decimal places rad s

0 5T Y sine cose W tane 4T O sine cose tane csc A sec cote CSC sece T cote

2 Using the method of the unit circle find the 6 trigonometric function values for an 5T angle of Draw a diagram and show everything including the reference 6 triangle with sides reference angle etc Circle your answers Leave answers as reduced radicals no decimals

7 A water molecule is made up of one oxygen atom O and two hydrogen atoms H The bonds between the oxygen and hydrogen atoms make the molecule triangular Calculate the angle formed at the oxygen molecule C 3 T2 pm picometre I H 96 pm 96 pm 151 8 pm 8 Two buildings are across the street from one another The shorter building is 18 m tall From the top of the shorter building the angle of elevation to the top of the taller building across the street is 400 and the angle of depression to the bottom of the building across the street is 420 How tall is the building across the street Draw a H

6 A group of mountain climbers are using trigonometry to determine the height of a mountain From point A the angle of elevation to the top is 29 A person is directly in front of point A and measures the angle of elevation to be 35 to the top of the mountain If point A and B are 8 2 m apart how high is the mountain C 3 T 2

3 Determine the unknown in each of the following triangles A 6 b a 18 36 4 Determine the measure of ZQ A 3 X 16 5 Determine the value of x in the following triangle A 3 R 8 2 75 10 11 124 3 10 1 28 1 Q

2 For each of the following triangles state the name of formula from above you would use to find the missing side length or angle K 6 a d 8 2 75 12 43 10 1 b e I X 27 3 41 77 X 15 c f 7 X 10 12 X 5

1 Use the legend to indicate which formula would be required to solve for the unknown variable in the triangles below Record your answers in the table below T 37 56 Triangle Formula 15 30 19 50 1 N X 2 X 19 2 17 14 8 3 12 15 4 20 8 39 X 37 19 22 5 18 3 27 25 7 8 C T SL CL PT Pythag Theorem sin COS 8 tan Sine Law Cosine Law

Normal text Calibri 7 ol Q GO 2 Use the Cosine Law to determine the value of x in the following triangle 20 46 3 Use Sine Law to determine the value of x in the following triangle 17 30 56 X 37 4 From two different tracking stations a weather balloon is spotted from two different angles of elevation 510 and 750 respectively The tracking stations are 15 km apart Determine the distance from the balloon to the tracking station furthest away tE m

Question 5 5 points Delia is flying a kite that is 23 m high above the ground The string of the kite is 30 m long What angle does the string of the kite make with the ground assuming that Delia is holding the string at ground level Include a diagram as part of your solution 5 marks Scan and upload your image of your diagram and work to google drive

Find the measure of the unknown angle labelled as x in the following triangle Round to the nearest full degree P Q L 32 24 25 26 33 cm Question 2 2 points Find the measure of the unknown side length labelled as x in the following triangles Round to two decimal places M 33 m 48 42 cm 47 m N 1222 36 34 96 R

Write the equation of the tangent line to the curve at the indicated point As a check graph both the function and the tangent line y x 4x 10 at x 1

7 Determine the missing side length of each triangle using SOH CAH TOA a b G 1 X 7 641 7 361 291 12 X 23 8 The angle of elevation to the top of a post from a point on level ground 38 m away is 33 Find the height of the post

A ship was sighted from a lighthouse on a foggy night When the ship was first sighted the bearing of the ship was N 15 E The ship then sailed for 8 9 miles due south The new bearing was N 29 E Find the distance between the ship and the lighthouse at each location The ship was first sighted at miles from the lighthouse Round to one decimal place as needed The new location of the ship was in SCEN miles from the lighthouse pooded

The motion of the collar at A is controlled by a motor B such that when the collar is at SA 3 ft it is moving upwards at 2 ft sec and slowing down at 1 ft sec Find a The velocity of the cable as it is drawn into the motor B at this instant b The acceleration of the cable as it is drawn into the motor B at this instant Solution Answer Vc VB 1 20 ft sec ac aB 1 11 ft sec a SA A 4 ft B PREPARE Fe Octave script FOR

1 Find a simplified expression for tan cos

Use your calculator to evaluate cos 0 84 to at least 3 decimal places Give the answer in radians

3 2 7 T 2 3 2 1 1 2 The graph above is a graph of what function Oy cos x Oy tan x Oy sin x Oy csc x Oy sec x Oy cot x 2 3 2

6 y 5 11 4 3 2 6 5 4 3 2 1 1 I 2 3 4 5 I P B S 4 Write an equation for the function graphed above 6