Trigonometry Questions and Answers

Two cars leave the same parking lot with one heading north and the other heading east After several minutes the northbound car has travelled s kilometers and the eastbound car has travelled 15 kilometers Measured in a straight line how far apart are the two cars 23 kilometers 7 Kilometers 17 kilometers 289 kilometers

phasors 10 j5 3 j6 15 j25 24 j30 36 j18 100 j250 300 j250 820 j320 241 j520

Find the rectangular form of the following phasors P 10 0 45 P 5 0 30 P 25 0 60 P 54 0 90 P 65 0 34 P 95 0 56 P 250 0 20 P 8 0 42 P 35 0 65 P 150 0 15

2 2 points Determine the length of FG to the nearest tenth of a centimetre a 36 1 cm b 33 4 cm F 30 c 35 0 cm G 65 12 cm E H d 32 6 cm

16 4 points Determine the amplitude the period the phase shift and the vertical shift of the function y 3 sin x 50 2 with respect to y sin x Amplitude Period Phase Shift Vertical Shift

There are five cats and seven dogs in a pet shop Four pets are chosen at random for a visit to a children s hospital What is the expected number of dogs chosen 7 12 7 3 7 4 none of these you can t have fractions of a dog

Find the angle A using the given right triangle Round off the results according to the table below Measurements of Angle to Nearest 1 0 1 0 01 Find angle A A Accuracy of Trigonometric Function 2 significant digits 3 significant digits 4 significant digits GOLOB 31 7 102

Find 0 for the given trigonometric function Round off the results according the provided table cot 0 0 0873 Select the correct choice and if necessary fill in the answer box to complete your choice OA 8 Do not include the degree symbol in your answer Measurements of Angle to Nearest 1 0 1 0 01 Accuracy of Trigonometric Function 2 significant digits 3 significant digits 4 significant digits

ion f x x for 0 x for 7 x for obtain the Fourier series of the x n interval x 27 to x 3 x 2

For an arc length s area of sector A and central angle 0 of a circle of radius r find the indicated quantity for the given value X r 4 63 in 0 s C

Determine the signs of the given functions tan320 cos157 The sign of tan320 is

Simplify 5w sin w to an expression involving a single trigonometric function cos 5w cos w Question Help Video Check Answer

Not Sa 4 37 2x IT 67 4 3 2 4 5 6 37 47 Sm Find a sinusoidal function that matches the given graph If needed you can enter T 3 1416 as pi in your answer otherwise use at least 3 decimal digits f x

Rewrite 1 sin x 2 cos x as A sin x p A 11 Note should be in the interval T T Question Help Video Check Answer

Which angle is not in the set of all angles described by 2nk O 17pi 8 O 31pi 8 O all choices here are coterminal O pi 8 O 15pi 8

15 Two boats at location P and Q are being tracked by a satellite located at R Using the information in the diagram find the distance between the two boats PQ to the nearest kilometre A 5 P 10km 107 15km

14 Ted hit a baseball The height h of the ball above ground in metres at any time t in seconds is given by the equation h 5t 20t 1 Complete the square and express h in the form h a t p q Then use your answer to answer the questions below A 10 a Determine the maximum height reached by the ball b How long does it take the ball to reach its maximum height c From what height above the ground did Ted hit the ball

11 A pine tree casts a 31 meter shadow when the angle of elevation from the ground to the top of the tree is 40 Find the height of the pine tree to two decimal places Include a diagram A 4

Solve the right triangle with B 49 9 and c 22 9 Round off the results according to the table Measurements of Angle to Nearest Accuracy of Trigonometric Function 0 19 0 01 2 significant digits 3 significant digits 4 significant digts Select the correct answer below and if necessary fill in the answer boxes to complete your choice OA A a OB There is not enough information to solve the triangle CIC Do

Given the triangle to 4 decimal places 19 33 Question Help Video Submit Question 27 x find the length of side z using the Law of Cosines Round your final answer 1

Given the triangle drawn to scale A 16 Submit Question A 12 9 find the measure of angle A using the Law of Cosines Picture is not Q degrees Give your answer accurate to at least one decimal place Question Help Video

force needed to lift the machine that has a weight of 10 kN 3 m 2 m 10 kN A 20 Prob 3 61 cables 1 25 m 1 25 m

1 2 2 F X n 2 2 Which of the following is the double component of signal x d 2 2 2

X t 2 e l an e b C d temel Derivodu nedir

How tall is a building that casts a 67 ft shadow when the angle of elevation of the sun is 29 The building is ft tall Round to the nearest foot as needed 29

Solve the right triangle with B 49 6 and c 23 1 Round off the results according to the table below Measurements of Angle to Nearest 1 0 1 0 01 Accuracy of Trigonometric Function 2 significant digits 3 significant digits 4 significant digits m Select the correct answer below and if necessary fill in the answer boxes to complete your choice OA A b B There is not enough information to solve the triangle Points 0 of 1 b

How tall is a building that casts a 66 ft shadow when the angle of elevation of the sun is 32 The building is ft tall Round to the nearest foot as needed 32 660

Determine the signs of the given functions sin25 cos 199 GELER

To get a good view of a person in front of a teller s window it is determined that a surveillance camera at a bank should be directed at a point 24 4 ft to the right and 14 6 ft below the camera as shown in the figure to the right At what angle of depression should the camera be directed What is the angle of depression A 2440

Find the exact expressions for sin 8 cos 0 and tan 0 sin 0 P 0 m

Solve the right triangle A Round to four decimal places as needed a cm Round to three decimal places as needed cm Round to three decimal places as needed XXX 42 0899 a

Suppose ABC is a right triangle with sides of A lengths a b and c and right angle at C Find the unknown side length using the Pythagorean theorem and then find the values of the six trigonometric functions for angle B Rationalize denominators when applicable b 2 c 5 b B The unknown side length a is 21 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Rationalize the denominator 2 sin B Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Rationalize the denominator cos B Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Rationalize the denominator

Sketch an angle 0 in standard position such that 0 has the least possible positive measure and the point 0 1 is on the terminal side of 8 Then find the values of the six trigonometric functions for the angle Rationalize denominators if applicable Do not use a calculator Choose the correct graph below OA Ay OB A Q Q OC

Find a value of 0 in the interval 0 90 that satisfies the given statement sin 0 0 68131374 02 0

7 What is the phase shift and direction of the cosine curve y 2cos 0 5x 100 2

A pilot looked out his window and saw an airport He estimated it to be at a 7 degree angle of depression while his plane was at an altitude of 1 855 miles How far in miles was the plane from the airport at that moment see distance to the airport in figures Airport distance to airport 7 Altitude

Solve AABC if a 7 cm b 8 3 cm and c 9 2 cm

Calculate the missing side lengths in the following triangle 42 Y 75

Calculate the area of the triangle shown to 1 decimal place Show all your steps 50 0 m 36 18

14 Determine equations to model each of the following sinusoidal functions 4 K 14 4A a b 200 400 540 440 420 360 309240 180 4 20 D 60 120 183 240 300 SHO A wim

60sin x 360 120 2 8 Determine the period of the function y 60 sin K

13 19 Sketch the function h x 4 cos 2 x 30 Include an appropriate scale on both axes

131 Sketch one cycle of the graph of y 3 sin x 90 Include an appropriate scale on each axis K

13 A 19 Sketch the function h x 4 cos 2 x 30 Include an appropriate scale on both axes

6 The depth of water h in metres in a given location on a given day at hours after midnight canbe modelled using the sinusoidal function h t 1 8 cos 30 1 2 5 7 a What are the maximum and minimum depths of the water b Determine a time at which low tide occurs c What is the depth of the water at 8 PM

8 Determine the period of the function y 60 sin sin x 360 12 120

The Cosine Law is valid for any triangle but it is only useful if you are given To determine missing side lengths in AABC a b c 2bc cos A b c or To determine missing angles ZA cos b c a 2bc 2B ZC

cm b APQR given ZR 112 p 31 2 cm and r 45 0 cm

34 and c 12 0 cm a AABC given ZA 42 ZC 34 and c

To determine missing side lengths in AABC a b c 2bc cos A b c To determine missing angles b c a 2bc ZA cos 1 2B 2C