Trigonometry Questions and Answers

6 Determine length z in each triangle Give the length to the nearest tenth of a unit a 61 ZO b A 13 0 mm N 29 7 8 cm c 2 mm 2

e g 2 A 2 m long ladder is leaning against a wall The ladder makes a 68 angle with the ground How far up the wall does the ladder reach

Properly labelling a right triangle C B Use SOH CAH TOA to build your ratic sinC cosC tanC sinB cosB tanB

the farm Stove who 15 5 feet tall notices that when his shadow is 9 ft long the shadow of the silo is 99 ft long How tall is the silo Note that the diagram is not to scale The silo is ft tall

Find the angle B Leave answer to 1 decimal and do not provide units a B 7 a 93 7 cm b 46 6 cm C b a

tee Pac 7 x 2 y 6 5 N 7 unter 9 x 2y 16y 31 AJ 11 x 2y 4y 2 As alldad 5 6 8 x 12 x 2y 1 3 2y 1 S Ay F 2123 2 Dix 3 10 x y 2y 4 Ay 2 245 Y 3 41 X 25830 23A 101 2 X2 2 4 1 x 3 F2017

You just loaded data from a remote source into your notebook To begin you would like to view a summary of your data in order to get a sense of the number of dimensions the number of unique cell values for each column the most common value and its frequency for each column Which package would you expect to have a ready made method for your goals O Numpy O Pandas O Matplotlib Seaborn

Two trucks leave a warehouse at the same time One travels due west at an average speed of 48 miles per hour and the other travels due east at an average speed of 45 miles per hour After how many hours will the two trucks be 558 miles apart

The measured the angle of el of a tree and round it was 38 She the angle then walked 25mg towards the tree and measured again of clevation to be bo a sketch the diagram buse ascale of 10m to represent Tom to draw the diagram accurately c Find the height of the tree d find the total distance to the botom of the tree from this initial position

The angle of elevation of the top of a r di most from a point 53m from Aishase on ground level is blofind the height up the mant a

What is a valid expression for tan A A x B 1 0000 A C 1 x D 1 620 A 450 X 450 00

11 1 point Under which condition s can the cosine law be used a three sides lengths are given b two sides lengths are given and an angle opposite to one side is given either a or b d none of the above

5 1 point The axis of the curve of a periodic function is the maximum value plus the minimum value

6 1 point The period of the sine function is 360 and the amplitude is 2

3 1 point In right AABC with right ZA B cos

3 Find the values of t in 0 27 that make the equation true Consider cott

The area of the triangle below is 25 37 square feet What is the length of the base 5 9 fr AN

Let cot2 u cos u cos u Find the solutions of the equation that are in the interval 0 2 COP 0 COSU COSO

A small plane lands at a point 276 miles east and 97 miles north of the point at which it took off Find the distance the plane flew and the direction Distance Direction Question Help I Norrago instructor miles degrees North of East

In AABC B 90 b 17 5 cm a 12 3 cm Solve the triangle 3 K include a diagram as part of your solution

Enter the ratio as a fraction in lowest terms 80 minutes to 88 minutes

Determine an equation for the graph to the right The equation of the graph is y Type an expression using x as the variable FIN 1 R

5 Q Find the circumference of the circle pictured above Round your answer to the nearest hundredth

The diagram shows points A B C and D on level ground AD 50 m AB 116 m BD BC and BAC 35 B Calculate T 116 m 135 50 m D i the length of BD ii the length of CD iii the shortest distance of B from line AC C

y 6cos x Which of the following is the correct graph of the function y 6cos x OA 21 Q OB 2 12 the 2n 27 27 57 O D 12 2x

For 4 6 find the length of the missing side Round to the nearest tenth if necessary You must show all of your work 4 5 17 6 3 13 2 4

Find the exact value of the trigonometric function given that sin and cos Both and are in Quadrant 1

The figure displays a unit circle and an angle of 1 radian The tick marks on the circle are spaced at every two tenths radian Use the figure to find a positive angle whose sine is 0 55 Find one positive angle whose sine is 0 55 One angle is Type your answer in radians Type an integer or a decimal rounded to one decimal place as needed Ay 101210 0 8 radian radian 0 6 radian 0608 0 4 radian 0 2 radian X 6

igle of radian The tick marks on the circle are spaced at every two tenths radian Use the figure to find a positive angle whose sine is 0 55 Find one positive angle whose sine is 0 55 One angle is 0 6 Type your answer in radians Type an integer or a decimal rounded to one decimal place as needed Try again Recall that for any real number s represented by a directed arc on the unit circle sin s y X 2 1 0 8 0 6 0 4 0 2 10 8 radian 5 0 6 radian radian 01204016 08 0 4 radian 0 2 radian X 6

d Equation of graph 3 Graph y 3 cosx Label your increments on the fat boxes with darker lines I 117 NEW N AR

0 Determine the value s of 0 for 0 0 360 sin 0 3 2 b 4 cos 0 6243

irections For each of the questions in this section show all your work for full mark 4 2 points An airplane is flying at an altitude of 6000 m The angle of depression from the airplane to the airport is 3 7 Determine the direct distance from the airplane to the airport to the nearest kilometre

2 3 points Determine x to the nearest tenth of a millimetre D 25 30 mm 12 52 56 259 B 215 45 X A

sin x cos x sin x cos x O True O False

Solve each triangle If answers are not exact round off to the nearest hundredth 1 108 120

1 cos x 1 cos x 1 s x 1 cos x True O False

13 1946891450771 9 42477796076938 At least one of the answers above is NOT correct 1 1 point Consider the pictures below Click on the pictures to see them more clearly Find the exact length of each arc intercepted by the given central angle If needed you can enter as pi 7 6 arclength 2 3 4 3 21TT 5 3 21pi 5 incorrect 1 correct

In AXYZ ZY 90 and ZX 55 ZZWY 82 and XW 9 7 Find the length of WY to the nearest 10th X 55 9 7 W 82

In AXYZ ZY 90 and ZX 60 ZZWY 83 and XW 1 5 Find the length of ZY to the nearest 100th X 60 1 5 W 83 Z Y

In AXYZ ZY 90 and ZX 67 ZZWY 70 and XW 28 Find the length of ZY to the nearest 10th 67 28 W Z Y

For the value of s below use a calculator to find sin s and cos s and then use the results to decide in which quadrant an angle of s radians lies s 74 sin s Round to four decimal places of pooded

Complete the table with exact trigonometric function values Do not use a calculator 0 135 0 sin 0 2 2 135 sin 0 2 2 cos 0 2 2 tan 0 tan 0 cot 0 cot 0 sec 0 2 cos 2 2 Simplify your onewers including opy radicale Ilse integers or fractions for any pu sec 0 csc 0 2 2 csc 0 2 ore in 1

Find the exact values for sin 0 cos 0 and tan 0 0 3 sin Simplify your answer Type an integer or a fraction 4

f Describe the transformations from y sin x stretching shrinking shifting etc 2 Identify the graph of the form y sin x and its features 11 4 c Amplitude TT 4 11 2 b Period 317 4 S4 c Increment

4 The period of the function shown is approximately AA 2 Am M 0

Sketch an angle 8 in standard position such that 0 has the least possible positive measure and the point 6 8 is on the terminal side of 0 Then find the exact values of the six trigonometric functions for 8 Choose the correct graph below O A Ay Q 5 B O B Ay M Q OU C O C Ay

If mGM 32 and mVR 94 find m B B G M R

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In Exercises 5 7 find the arc length of AB 6 5 6 cm 60 B B 150 p A 18 in 7 30 P 28 ft B

A b 3 13 50 points Find the exact value tan 30 sin 45 a 2 C