Trigonometry Questions and Answers

Macmillan Learning Assume that sin x sin x y 3 and sin y 4 7 where T 3 x and y 2 Calculate the indicated function value 2 sin x y Give an exact answer Use symbolic notation and fractions where needed

Fill in the blanks to show the identity cos x cos x Use appropriate sum formulas cos x Y cos x

Find the tangent and cotangent of 195 Note that 195 150 45 Use sum or difference formulas involving special angles or angles whose reference angles are special angles Give exact answers Use symbolic notation and fractions where needed Simplify your answers completely tan 195 cot 195

sin 19T Find the sine and cosine of 12 whose reference angles are special angles Give exact answers Use symbolic notation and fractions where needed Simplify your answers completely 197 12 19T 12 Note that 4 T 3 4 Use sum or difference formulas involving special angles c COS 927 12

y 3 ot 2x Od Points 5 b y 5 sin 2x Period 5 Amplitude Phase Shift

4 Solve each equation on the interval 0 0 2 a 2 sin 0 sin 0 1 0 b sin 0 cos 0 1 cos 0

6 Find the exact value of tan 285

6 Find the exact value of tan 285

10T Find the length of the arc of a circle of radius 11 meters subtended by a central angle of 7 Round the answer to two decimal places 10 radian

T Complete the passage to express sec t in terms of csc t if 0 t 2 sec t csc t csc t 1 csc t V csc t 1 csc t V csc2 t 1 csc t csc t 1

On 5 of 13 Macmillan Learning 4 Assume s is an angle with sin s t is an angle with cos t 7 Resources cot ts 2 and both angles are between 0 and 3 Use this information together with appropriate identities to calculate cot f s Give an exact answer Use symbolic notation and fractions where needed T 2 Check

Complete the passage to express the cosine in terms of the cotangent and the sine cos t cos 1 sin t 1 cos x sin 1 cos t 1 sin x X

Verify the cofunction identity c 1 2 1 sec Refer to the triangle in the figure 2 C csc t T a Fill in the blank to prove the given identity sec t csc t

Fill in the blanks to determine whether the function f t tan t sin t is even or odd Therefore the fu tan t sin t tan t sin 1 tan t sin 1 tan t sin t

Solve the given equation Enter your answers as a comma separated list Let be any integer Round terms to three decimal places where appropriate If there is no solution enter NO SOLUTION 2 sin 20 3 sin 0 0 80 cos 3 X

Question 3 of 13 3 7 Express numbers in exact form Use symbolic notation and fractions where needed cos x 2 Use a trigonometric identity to find cos s x 7 7 7 if sin x 2

Compute the degree of the curve D given the radius R as R 286 479 feet using the arc definition O 25 degrees O 17 degrees 20 degrees O 15 degrees D Question 2 1 pts Compute the degree of the curve D given the radius R as R 573 686 feet using the Chord definition O 6 degrees

Inn Provide your answer below 8 mi Shoreline 10 mi A visitor is staying in an inn that is 10 miles west of the closest point on a shoreline to a coral reef The coral reef is 8 miles due north of the shoreline The visitor plans to travel from the inn to the coral reef by running and swimming If the visitor runs at a rate of 5 mph and swims at a rate of 2 mph how far should the visitor run to minimize the time it takes to reach the coral reef Round to two decimal places

assign Problem 20 1 point Find a vector that is perpendicular to the plane through the points A 1 1 3 B 1 5 3 and C 0 5 1 V

b Determine the value of C 100 What does this number represent c Determine the value of n when C n 5000 What does this number represent Answers a C n 25m 1000 b 3500 c 160 5 Which sets of ordered pairs represent functions Identify the domain and range of each set of ordered pairs a 1 3 2 6 3 9 4 12 b 1 0 0 1 1 0 0 1 c 2 3 4 5 6 7 8 9 d 0 1 0 2 1 2 0 3 1 3 2 3 6 Write in function notation

1 Suppose that cos x and cos x x 1 2 7 3 sin x 2 2 Make use of the following facts The period of the sine and cosine is 27 The sine is odd and the cosine is even x 1 cos x for all x Express numbers in exact form Use symbolic notation and fractions where needed Simplify your answer completely R Find the value of sin x 2 3

1 point Find two vectors and 2 whose sum is 3 2 where V is parallel to 5 2 while U2 is perpendicular to 5 2 U1 V and

4 Evaluate the integral 7 points 2 2 xy SSS cos 1 dz dy dx

Problem 6 Two people are standing on opposite sides of a small river One person is locate dat point Q a distance of 35 m from a bridge The other person is standing on the southeast corner of the bridge at point P 2 radians Use this information to The angle between the bridge and the line sight from P to Qis 5 determine the length of the bridge and the distance between the two people Include a diagram

1 If the angle of elevation is 42 what is the length of a shadow on the level ground of a man who is 6 1 ft tall Include a diagram

Solve the given equation Enter your answers as a comma separated list Let k be any integer Round terms to two decimal places where appropriat cos 8 0 24 0 X 0 rad List six specific solutions rad

Macmillan Learning The value of one of the trigonometric functions of an acute angle t is given Find the values of the other five trigonometric functions of t 29 20 Express numbers in exact form Use symbolic notation and fractions where needed sec t sin t tan t csc t cos t cot t

Millan Learning Let sec t 3 and cot t be negative Find the values of the five remaining trigonometric functions Express numbers in exact form Use symbolic notation and fractions where needed sin t tan t csc t cos t cot t

Verify the identity Simplify your answers completely 7 sin t 7 cos t tan t Use a Reciprocal Identity and then simplify 7 sin t 7 sin t tan t cos t 7 sin t cos t

the IB SL formula booklet Round to 3 s f if not otherwise specified The following diagram shows a park bounded by a fence in the shape of a quadrilateral ABCD A straight path crosses through the park from B to D AB 85 m AD 85 m BC 40 m CBD 41 BCD 120 diagram not to scale 85 85 B 1415 40 1 I 120 C VICT PUIGUTTE Calculate the size of angle B D correct to five significant figures 2 The size of angle B D rounds to 77 correct to the nearest degree Use B D 77 for the rest of this question 2

The equation A t 50000 06t a Find a formula for b Find and interpret A 9 Include appropriate units C Compare the approximation of 515 to the actual change Report your answer to two decimal places dA C gives the balance after t years of an initial investment of 5000 dollars which pays 6 00 compounded continuously

Some angles and the length of a side of a triangle are given in the figure The altitude of the triangle is included C 46 13 perimeter A HA B Find the area and perimeter of the triangle Note that you may wish first to find some of the unlabeled sides Express numbers in exact form Use symbolic notation and fractions where needed units area square units

A drone is flying due north at a constant speed An observer uses a laser to locate the drone due east at a distance of 120 feet One minute later the observer rotates the laser by 40 to locate the drone See the figure 40 speed Observer How fast is the drone traveling Give your answer to the nearest whole number I 120 Path of drone Enter numeric value feet per minute

Vrite the equation of a sine or cosine function to describe the graph 2x 3 2x 3 2x 8x 3 10x 0

In order to get characteristic X rays using Mo as a target metal what is the minimum voltage to be used O 10 kV O 15 kV O 20 kV O 25 kV O Any voltage

Q2 Solve for z in 8z 2i 3iz 1 3i 2 5 45 and write the final answer in polar form You may use the calculator 8z zi 3iz 3 15pts 15 135 22 1 3 8 3 5 45 3 3 15 135 5 45Z I 15 135 22 1 8 31 5 45 0 29 1 262 1029 103 09 3 15 135 10 61 10 612 l 3 544 3 541 3 11 61 12 611 11 54 6 541

4 What are the lengths of AB and AO Show your work and round if needed

15 points A waveform r t 10 cos 1000xt 3 20 cos 2000xt 6 is to be uniformly sampled for digital transmission a What is the maximum allowable time interval between sample values that will ensure perfect signal reproduction b If we want to reproduce 1 hour of this waveform how many sample values need to be stored

7 What equation is represented by the graph O X

1 What are the sine and cosine of 12

16 ft ladder leans against the side of a house The angle of elevation of the ladder is 67 How high is the top of the ladder from the ground Round your nswer to the nearest tenth 16 67 H ft

The architect draws a 30 60 90 right triangle to show the location of a car on the Ferris wheel with respect to its center O 3 What are the sine and cosine ratios for ZO 0 center Unit 5 QPA location of car 30 4 What are the lengths of AB and AO Show your work and round if needed

Use any method to evaluate the integral tan 213x S S csc 13x tan 213x csc 13x dx dx

b sinx cost 4 ise six cos x

Find the answer for the multiplication of the following 3 1 0 2 O 01 1 1 3 1 n 21 0 2 06 02 O Not possible to find this multiplication one of th th

5 Find the relating angle to the given one Related sin 240 to the sine of an angle of the first quadrant Select all correct statements The angle 240 is in quadrant III Its related angle is 30 sin 240 sin 240 180 The angle 240 is in quadrant III Its related angle is 60 The angle 240 is in quadrant III Sine is positive in quadrant III 3 sin 240 sin 60 and so sin 240 3 2 The angle 240 is in quadrant IV Sine is negative in quadrant IV sin 240 sin 60 and so sin 240 3 The angle 240 is in quadrant III Sine is negative in quadrant III

4 Calculate the value of sin 15 3 1 2 2 O O O O O 3 1 2 2 3 1 2 2 3 1 2 2 None of the other options is correct

2 Find the value of cos 330 Sellect all the correct answers cos 30 4 4 cos 30 000 is

5 State whether the sign of cos 100 is positive or negative O Positive O Negative

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