Trigonometry Questions and Answers

What is the first step when finding the missing side length of a triangle O Label Hypotenuse Write down tangent ratio sohcahtoa O Label right angle

IF 0 arc cotx then O cot 0 and 0 0 2 O cot0 x and 0 k k integer O cot0 and 0 0 O cotx and 0 0

inscribed in circle M Solve for x and y I L X 110 x 44 M 74 J y 48 y K

5 Graph 2 periods of y 3 cot 3x with 3 points for each period Name the amplitude period and phase shift Label asymptotes and amplitude

following right triangle find sin A cos A tan A and sin B cos B tan B X sin A cos A tan A sin B cos B tan B B 3 x C X A

nd 32 Part 1 of 3 a Find the percentile rank for a score of 42 A test score of 42 is equivalent to the 55 th st nd rd Part 2 of 3 b Find the percentile rank for a score of 47 A test score of 47 is equivalent to the 80 Part 2 3 Part 3 of 3 th st nd rd c Find the percentile rank for a score of 43 percentile percentile 41 36 30 48 49 39 45 31 47 40

Find the value of the 6 trigometr function 3 5 7 9

from one unit to ng happens Conventin another measurement savared use differoppens when companies systems In Europe the acceleration due to gravity Oh earth is 4 8 meters per second 4 8m s 2 In some companies in the USA the same is 32 feet acceleration 32 ft s 2 Which choice below shows the correct conversion between European and American arz 3 28 units Assume in feet one meter A 4 85 2 3 2847 3 0 X5 f x5 B 4 85 3 28 36005 46 116 000 fl 4 8m2 3 28ft 52 32 ft S ft 0 4 852 3 28 3 0 et m

Let 0 arcsin then O 0 0 0 and sin0 and sin0 3 5 0 0 4 and sin0 3 and sin0 3 O 0 2 and sin 0 3 3 3 2 2

a sin 5 3 2 1 2 b arctan cos cos 3 c arccos cos

Convert 5 8 from radians to degrees Round to nearest tenth

Solve for x 0 x 2 sin 2x cos x

1 Solve the following triangle Round side lengths to the nearest tenth of a centimeter and angles to the nearest degree A B 11 38 10 C C 14 M

6 5 4 3 2 5 A 3 2 1 ON 3 7 La 3 4 5 6 The graph above is a graph of what function

K 4 3 2 1 2 1 1 2 3 4 41 What is the slope of the line 2 22 3 4

Balance a ration for 14 CP DM using cracked corn and soybean meal 44 Soybean hull are fixed in the ration at 10 of the DM What is the equation used to solve this problem

Use primary trigonometric ratios to determine the value of x to one decimal place b X 5 cm 22 m 53 12 cm d X 25 8 cm X 40 m cr

2 The Leaning Tower of Pisa in Italy leans at an angle of about 84 7 The figure shows that 171 feet from the base of the tower the angle of elevation to the top is 50 Find the distance to the nearest tenth of a foot from the base to the top of the tower 84 7 50

4 A fire is spotted from two ranger stations Station A is 4 miles west of Station B From Station A the fire is 35 east of north and from Station B the fire is 25 west of north See the picture below not necessarily to scale Find the distance between the fire and each station Which station is closer to the fire 35 11 25

Without using a calculator state the exact value of the following trig functions for the specified angle an 0 a tan b tan 5 T 6 c tan 0 0 0 1 57 0 6 7 g tan 7 0 d tan 11 6 0 6 f tan e tan 13 h tan 6 11T 6 5 0

Given the angle 117 6 To which quadrant does belong Write your answe as a numerical value Find the reference angle for IN RADIANS 0 Find the point where intersects the unit circle

First determine the quadrant for then find x y and r and finally give all six trigonometric ratios forgiven the following information e lives in quadrant y T sec 0 11 and tan 0 0 1 sin 0 2 cos 0 3 tan 0 4 sec 0 5 csc 0 6 cot 0

Problem 2 1 point 10 cos 0 tan 0 Find the value of the six trigonometric functions of 0 where is the angle formed by the positive x axis and the line segment from 0 0 to 6 5 sin 0 sec 0 csc 0 cot 0 10 10 6 5 18

1 point 1 10 sec 0 Find the value of the six trigonometric functions of 0 where is the angle formed by the positive x axis and the line segment from 0 0 to 1 9 sin 0 cos 0 tan 0 csc 0 1 9 cot A

A plane is flying at an elevation of 33000 feet It is within sight of the airport and the pilot finds that the angle of depression to the airport is 19 Find the distance between the plane and the airport Find the distance between a point on the ground directly below the plane and the airport

To find the distance AB across a river a distance BC 280 is laid off on one side of the river It is found that B 105 and C 30 Find AB See the picture below Click on the picture to see it more clearly WAS Maw 246 1 188 w B Que

5 A 37 If angle B measures 37 and AC has length 5 find Angle C in degrees The length of AB The length of BC If you use a calculator to find a decimal approximation your answer must be accurate to at least 3 decimal places Just be sure that your calculator is set to degrees not radians You are also allowed to use the sine cosine and tangent functions in your answer instead of using a calculator

Use AB BC and AC as the side lengths sin B A cos B tan B sin C cos C tan C Remember that opposite and adjacent legs depend on which angle you re looking at

A Which side is the hypotenuse Which side is opposite of angle B Which side is adjacent to angle B Which side is opposite of angle C Which side is adjacent to angle C For each answer choose one of AB BC or AC B

Priya has planted a garden shaped like a right triangle She knows that one leg of the triangle is 5 meters long and that the angle formed by that leg and the ypotenuse is 50 If Priya wants to build a fence along the hypotenuse how many meters of fence will she need Round your answer to the nearest tenth 5m

The auxiliary equation for the given differential equation has complex roots Find a general solution 12y 12y 6y 0

17 If the central angle is 220 and the radius is 8cm the arc length is 117 9 A B 1760 C 27 5 18 The Exact Value of 2 sin 45 cos 45 A O C 1 B 90 D 30 7cm D 1

Graph of a function y f x is shown Evaluate S f x dx Show your solution y f x 3 2

The angle of elevation to the top of a building from a point on the ground 110 ft away from the base of the building is 45 How tall is the building tan 45 1 Round the answer up one decimal places

The terminal side is standard position contains the point 2 5

if m 30 degress and a 4 4 find c and round to the nearest tenth

mplify cos t sin t cos t sin t 2 sin 2t csc t to a single trig function

Are the expressions cos x y and cosx cos y equal Explain why or why not

Solve for the exact solutions in the interval 0 27 List your answers separated by a comma if it has no real solutions enter DNE 2 sin 0 2 cos 20

Solve each of the following triangles a 92 00 A 72 B 35 5 b 44 A 100 C 42

A person standing on the earth notices that a 747 jet flying overhead subtends an angle 0 45 If the length of the jet is 230 ft find its altitude to the nearest thousand feet Convert 75 degrees to radians 91 Convert radians to degree 17

12x 8 P Solve for x O 17 O 12 O 10 4x 4 e 50 D S R

P O 185 SO 170 O 153 R Find the indicated arc O 166 65 44 S

Determine the resultant r of the given forces Assume f acts in the positive x direction f acting due east with a magnitude of 16 N f acting due north with a magnitude of 12 N f3 acting due west with a magnitude of 8 N and f4 acting due south with a magnitude of 4 r 8 8

2 A plane is heading N57 E at 400 mph If a wind is blowing from N20 W at 42 mph find the direction and ground speed of the plane 392 7 mph N63 0 E 16 46 T

Sketch the graph of the following equations on the polar axis by making a table of values of 0 that are multiples of 45 a r 2 cos 20 b r 4 5 sin e

A hyperbola has its foci in F 1 2 and F 1 6 It also has a vertex in V 1 4 Find the standard equation the center the other vertex the equation of the asymptotes and the graph Center Standard Equation Asy with positive slope y Vertex 2 10 5 Asy with negative slope y 0 10 A hyperbola has its foci in F 1 2 and F 1 6 It also has a vertex in V 1 4 Find the standard equation the center the other vertex the equation of the asymptotes and the graph Center Standard Equation Vertex 2

Graph one full cycle for the the functions Find the range period amplitude if defined and note any reflections vertical or horizontal shifts a y 2 1 2 sin 2 3 x b y 1 2 2 sec 1 2 x

Use the information given about the angle 8 to find the exact value of the indicated trigonometric function No work no credit Do not use calculators No credit if using calculators to get the answer Rationalize the denominator if needed a Which quadrant is angle 0 in With the given information below draw the angle 8 in the corresponding quadrant in an x y coordinate plane b Show the half angle formula you use to find sin c Use a and b to find sin d Show how you determine the sign of sin tan 0 2 7 0 3 Find sin

Recall that an angle making a full rotation measures 360 degrees or 27 radians a An angle measures 205 degrees What is the angle s measure in radians 41pi 36 b An angle measures 5 radians What is the angle s measure in degrees degrees Preview 900 pi radians Preview 41 3 577924966588375 36 in radians is 900 radians c The angle angle formed from 0 4 turns around the circle in degrees is degrees Preview 286 4788975654116 Preview Box 1 Enter your answer as a number like 5 3 2 2172 or as a calculation like 5 3 2 3 5 4 Enter DNE for Does Not Exist oo for Infinity Box 2 Enter your answer as a number like 5 3 2 2172 or as a calculation like 5 3 2 3 5 4 Enter DNE for Does Not Exist oo for Infinity Box 3 Enter your answer as a number like 5 3 2 2172 or as a calculation like 5 3 2 3 5 4