Trigonometry Questions and Answers

gure to evaluate the function given that g x

Translate ork e the expression in rectangular form x

how that the given set of functions is orthogonal on the indicated interval Find the norm of each function in the set sin x sin 3x sin 5x 0 2 For m n For m n so that for sin sin 2n 1 x sin 2m 1 x dx 2 2 cos n m x 2 2 sin 2n 1 x dx lland 11 11 11 11 DI dx

In Exercises 25 and 26 verify each 25 sin 40 cos 0 4 sin 0 8 sin 0 26 cos 40 8 cos 0 8 cos 0 1 quadruple angle formula

x 151 98 olve for 12 4 300 3 4 9 8 7 6 5 2 1 2 NO 489 5 y g 6 7 8 9 7 Using the Coordinate plane above in which quadrant is point A located 8 We want the following inequality to be true What are possible values for x Give at least three answers C

An electric winch lifts a weight on the end of a 5 m jib pole Determine angle 0 for the position shown in Figure 3 7 m 5 m FIGURE 3 8 m

On the interval 0 2 determine which angles are not in the domain of the given functions What angles are NOT in the domain of the secant function on the given interval

Find the volume and surface area of a right triangular base pyramid that has side lengths 6m 8m and 10m The height of the pyramid is 13m and the slant height is 20m V 246 SA 264 SA 134 V 73 SA 305 V 104

A 10 foot ladder is leaning against the side of a house The angle it forms with the ground is 75 How high up the side of the house does the ladder reach

Determine the length of side C of the triangle shown in Figure 30 m 65 45 m FIGURE 2

26 of 30 1 point 16 17 Question Attempt 1 of 1 18 19 e figure below Karen is looking at a tree that e top of the tree is 38 The length of the tree of a foot

tion 4 of 30 1 point Question Attempt 1 of 1 2 3 identity x 1 sinx cos x 4 5 each Statement must be based on a Rule chose of the Rule

19 20 21 2 triangle ABC like the one below Suppose that intermediate computations to at least four decir more than one solution use the button labeled

Suppose that sina sin a Find the exact values of sin and tan 2 tan N R 2 81 a 0 11 2 7 5 and 270 a 360 3 Undefined X S JU

Homepage Northland 42 8 Points The graphs of 4 DETAILS 42 Select y Select W Assignment 12 Conic 1 and x 3 y 1 2 Select y Select 5 2 Select 42 4 Select Homepage N ica X M Speech 5 Submit Outl Ma 1 are given Label the vertices and foci on ead

Given that tanx 5 and sinx is negative determine sin 2x cos 2x and tan 2x Write the exact answer Do not round

DX 8 5x 10 3 Solve for x 74 7x 2 43 6x 15 12 Me 2x 5 11x 121 50 37 17X

For Problems 12 15 find x y and z Write your answer in simplest radical form 13 15 N 8 9 10 27 5

MATH 104 01 Colle U II U II answ uestion 5

U a C MATH 104 01 College Trigonometry 20445 Spring Semester 2023 B B Note Triangle may not be drawn to scale Suppose A 63 degrees and b 7 Find C a degrees b C Week 14

The red shape has been translated to the blue shape The translation is x A B C D E x y x 6 y x y x 4 y 4 x y x 6 y 6 x y x y 6 x y x y 6 5 4 3 4 5 2 5 0 6 5 4 3 2 1 0 3 2 5 6 2 2 4 3 1 2 2 2 3 4 3 1 2 2 4 3 2 4 5 2 5 0 X 4 5 6 3 2 5 4 5 6

Question 3 20 points Basic Trigonometry Determine the approximate value of x T 23 8 18 85 07 36 8 69 20 47 C wwwww A Question 4 20 points Basic Trigonometry Determine the approximate value of e

The rectangular coordinates of a point are given Find polar coordinates of the point such that r 0 and 0 0 2 0 2 The polar coordinator oro

Verifying a 30 60 90 Triangle Relationship Given that LABC is equilateral and AD bisects LA show that the side lengths of AADB are in a ratio of 1 3 2 1 Equilateral triangles are also equiangular so m A m B m C

NOMETRIC FUNCTIONS gonometry to find angles of elevatio ng rises to a platform that is 20 ft off

O TRIGONOMETRIC FUNCTIONS Coterminal angles Try Again Your answer is incorrect a Your answer is incorrect Answer the following

NS Translate ework Plot the point given in polar coordinates 2 Question 3 9

Write the expression as the sine cosine or tangent of an angle Then find the exact value of the expression tan tan 1 tan tan 3 5 3 1 tan 5 3 Write the expression as the sine cosine or tangent of a single angle 3 5 3 1 tan tan 5 5 5 tan tan 4 15 Type an exact answer using as needed Use integers or fractions for any numbers in the expression Find the exact value of the expression tan tan 4 15 3r 4 15 4 15 4x 15 tan 4 15 point s possible

The figure shows a 1250 yard long sand beach and an oil platform in the ocean The angle made with the platform from one end of the beach is 83 and from the other end is 75 Find the distance of the oil platform to the nearest tenth of a yard from each end of the beach The platform is about yards from one end of the beach and Use descending order Round to the nearest tenth as needed 83 75 1250 yards yards from the other

O ADDITIONAL TOPICS IN TRIGONOMETRY Solving a word problem using the law of cosines kwants to know the length of a tunnel built through a mountain To urements to find the length of the tunnel

O TRIGONOMETRIC FUNCTION Using a trigonometric rat x Round your answer to th

Verify the following identity tan tan x 2 sec 1 Which of the following statements establishes the identity O A tan 2 XX B tan 2 OC tan 2 sin 1 cos x 1 cos x 2 1 cos 2 tan a sec 1 tan x sec 1 tan a sec 1

In the following problem the expression is the right side of the formula for cos x B with particular values for x and B COS 7x 12 COS The value of x is The value of is 3 a Identify a and in the expression 7 12 7 T 3 The expression is cos sin b Write the expression as the cosine of an angle 7 12 T 4 sin c Find the exact value of the expression 7

Verify the following identity 1 cos2x 2 cos x To transform the left side into the right side should be changed to and the left side simp 1 2 cos x 2 cos x 1

4 Find the exact values of the five trigonometric ratios for tan a 5 and cos a 0 C 3 marks

5 A kite is fastened to the ground by a string that is 45m long If the angle of elevation of the kite is determine the kite s height off the ground T3 marks

5T 3 Determine an exact value for sin I cos 17 cot 6 K 3 marks

2 Determine the exact value of cos K 2 mark

5T 3 Determine an exact value for sin COS 117 6 I cot K 3 marks

Exercise 6 Let tan 0 3 with 0 in Ql and find csc 20 Draw a diagram

134 The divers entered the water 100 m away from the buoy The needed to repair t buoy s mooring cable at a point 30 m beneath the surface If they dove in a strai line to the repair point what was their angle of descent Hint Make a sketch of situation first Round to 1 d p

Jamie is helping his aunt make kites to sell at a craft fair Jamie s aunt gave him stacks of four different sizes of nylon triangles She asked him to sew them into kites She told him that he needs to use at least four triangles for each kite and the kites must meet the requirements shown in the figure to the right Jamie took a few measurements from these triangle shapes 25 A C cm 25 D 2 60 cm F AA 3 G After trying different arrangements Jamie discovered that he can arrange two of Triangle 1 and two of Triangle 2 as shown to make a kite 1 To add structure to the kite Jamie wants to secure rods along both diagonals What lengths of rods does Jamie need to cut Round to the nearest tenth and explain your reasoning M 144 2 M C1 O 2

Add the given vectors by using the trigonometric functions and the Pythagorean theorem F 154 0F 90 0 T 128 0T 160 0 Use Table to solve the problem

The right cylinder is inscribed into the right pentagonal prism with the base edges are 6 ft and the height 8 ft The volume of the cylinder is A B C D 78 15 ft 148 04 ft 428 51 ft 904 78 ft

Label all the vertices and foci on the graphs given for the ellipses in Exercises 2 and 3 a 52 42 Select O Select 5 4 3 2 1 y 5 3 2 1 1 2 3 5 1 2 3 Select 4 Select B X

the selection and choose the best answer They sent him back to her The letter came Saying And she could have him And before Not to Keep by Robert Frost She could be sure there was no hidden ill Under the formal writing he was in her sight Living They gave him back to her alive How else They are not known to send the dead And not disfigured visibly His face His hands She had to look and ask What was it dear And she had given all And still she had all they had they the lucky Wasn t she glad now Everything seemed won And all the rest for them permissible ease She had to ask What was it dear A From distrustful to concerned B From excitement to anger From optimistic to sorrow From sympathetic to defiant Enough Yet not enough A bullet through and through care High in the breast Nothing but what good And medicine and rest and you a week Can cure me of to go again The same Grim giving to do over for them both She dared no more than ask him with her eyes 19 Which phrases best describe the shift in tone from the beginning to the end of the poem How was it with him for a second trial And with his eyes he asked her not to ask They had given him back to her but not to keep 20 How is irony demonstrated in this poem A It displays the emotions felt by people who have loved ones at war It illuminates the reasons why the wounded soldier is allowed to come home before going back to war It brings about the idea of people not being free but belonging to someone else It shows how the in

rite the trigonometric expression as an algebraic expression in u and v ssume that the variables u and v represent positive real numbers cos cos u tan v 0

Translate rk Ques e triangle shown on the right and the given inf 4 A 80 find a c and B

Que the figure To find the length of the span o or measures the angle DAB to be 25 and feet to C and measures the angle ACB to o B

Questi that covers a sliding glass door that is 88 in he wall The purpose of the awning is to pre when the angle of elevation of the sun is mo nd the length L of the awning