Trigonometric equations Questions and Answers

But just as the Jedi Trainees use the lever to save their friends Vader The person with the longest lightsaber wins the duel duel Use your A B and C from the previous problem to determine blade lengths to 2 decimal places and the winner of the Your lightsaber Vader s Lightsaber Winner me IN 5c 92a 1 4 ft ft B 14 type either me or vader from the shadows emerges the one the only Darth

Like 7 80 Consider the triangle below Ho

For what values of on the interval 0 2n does f x 2 cos z zhave a horizontal tangent line Give your answers as exact values separated by commas

Find the exact value of sin cos Write your answer in radians in terms of 0 3 Undefined J 0 6

An airplane travels at 110 km hr for 2 hours in a direction of 230 At the end of this time how f south of the airport is the airplane Note Directions are given in degrees clockwise from north The airplane is kilometers south of the airport after 2 hours Round to the nearest integer

The observation deck of the Space Needle is 520 feet above ground The tip of the Space Needle is 85 feet above the observation deck An artist makes a replica 1 that is the height 100 of the

The acceleration of a vehicle can be expressed as follows du dt 3 6 0 06u The vehicle speed u is 30 ft sec at time To a Determine the distance in ft traveled when the vehicle has accelerated to 35 ft sec ft b Determine the time in s for the vehicle to attain the speed of 35 ft sec Enter the time after To S c Determine the acceleration in ft s after 6 sec Enter the magnitude 2

Point A is located 0 109 m away from a charge of 1 26 x 10 C Point B is located 0 504 m away from the charge What is the electric potential difference VB VA between these two points Number i Units

10 Given the ratio for csc find the remaining ratios sin 0 cos 0 tan 0 csc 0 sec 0 7 2 cot 0

Graph giv Le period phase shift and vertical shift of the function y sin x 1 3 4 2 4 Clear All Draw Period Amplitude Phase Shift 2 1 1 2 4 2 3 4 ww T 5 4 3 2 77

Graph the given function State the period amplitude phase shift and vertical shift of the function Y 4 sin x 2 T Clear All TU 2 4 3 2 1 1 2 3 Draw 2004 2 T 3

api phase shift and vertical shift of the function Y 4 cos x 2 T Clear All Draw Period Amplitude Phase Shift T 2 4 3 2 1 1 2 3 ww 2 3T

1 Dilate AABC by a scale factor of 3 where the center of dilation is at point O You will need a straight edge and a compass or some other measuring tool B

9 B 9 A 13 H 5 C ABC geninde AH 1 BC BH 9 cm HC 5 cm AC 13 cm oldu una g re sin BAC ka t r

Given cos 0 a and sin 8 b and is a reference angle Write the following in terms of a and E 1 a csc 0 3n cot 2 0 b sin 5 a sec 6n a cot

3 19 Determine the unstretched length of DB to hold the 40 kg crate in the position shown Take k 180 N m 2m 2 m D 3 m Probs 3 18 19

8 a Determine the measure of angle C to the nearest degree E 3 9 cm 7 cm B 46 529 b Determine the length of BC to the nearest tenth of a centimetre 9 Use Cosine Law to determine the length of e to the nearest tenth of a centimet 4 5 cm 10 cm C

13 Olivia has a pool slide that makes an angle of 34 degrees with the water The top of the slide stands 5 3 feet above the surface of the water How far out into the pool will the slide reach

Finish solving the triangle A ZA ZB 20 24 42 b degrees a b C C 13 Enter your answer as a decimal value You must be accurate to at least 3 decimal places Note that for these problems we are using degrees to measure angles Make sure your calculator is set to degrees instead of radians

10 A wire bolted to the ground 7 feet away from the base is helping a tree stay upright If the angle of elevation of the wire is 44 how long is the wire Round your answer to the nearest tenth

4 Represent a cosine function with an equation that has an amplitude of 3 a period of and a minimum value at 1 4 4 marks

0 sc n 6 c 0 c 0 18 t 0 IN All DOBIO 1 All HE A 110 7 1 MIL TXIL IN TOTE 101 IN IDE IN HITH 11 11 IH 11 11 11 14 1 10 1 0 10 170 HER TEK L EUR 131 HOT 100 21 101 14 11 NE 101 Th IN BIU HP 414 E K 414 K 10 11 IMI THE no U 1 1 11 1 11 17 MI nd the value of the six trigonometric functions of 8 where is the angle formed by the positive x axis and the line segment from 0 0 to 7 1 n 0 K 10 IN 18

Determine the domain of the function f x 5 x Choose the domain of f x OA 5 00 OB 00 00 OC 0 5 OD 0 5

An airplane is heading north at an airspeed of 700 km hr but there is a wind blowing from the northwest at 80 km hr The plane will end up flying 05 0243526902415 degrees off course The plane s speed relative to the ground will be 645 91333823285 km hr

27 The density of a wax candle in the shape of a cube is 2 7 grams per cm If the mass of the candle is 475 grams what is the side length of the candle Round your answer to the nearest tenth of a cm CITY

The pitch of a roof is given as a single digit such as 7 pitch This actually means this roof has a rise of 7 feet for every 12 feet of horizontal run What is the angle of a roof with a pitch of 7 Round to the nearest 0 1 88 1 degrees 0 6 degrees 35 7 degrees 30 3 degrees

14 1 point Find the missing parts of the triangle A 45 b 10 c B 90 10 7 14 14 7 07 b A

Find the value of the following 17 tan cos 5 15 Give your answer in lowest terms Rationalize the denominator if necessary Enter the number that belongs in the green box Enter

Find the value of the following sin 1

2 Graphing a cosine function using five key points 24 points 470 y cos 2x 3 3 1 Use the even odd property to rewrite the function in an equivalent form in which the coefficient of x in the argument is positive 3 points 2 State the amplitude 3 State the period 4 State the phase shift 5 State the domain 6 State the range 2 point 7 Find the x coordinates of the five key points complete the chart 3 points 1 point 2 points 2 points 1 point 7 Find the x coordinator of the fire l

7 10 points Find the all solutions of this equation in the interval 0 2 2 tan 0 3 tan 0

Solve * Ut = kuxx - iux, -∞0<x<∞, t>o U(x,0) = f(x)

Find all solutions (in radians) of the given equation on the interval [0,2n) * (5 Points) 3+9 cosx = 5 sin? x−6 7-cos-¹(); 7+ cos¯¹; π -4/5;-1;π π; cos ¹(4/5) None of these expressions I don't know.

Determine the open intervals on which the graph is concave upward or concave downward. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) y = 7x-5 tan x, (-π/2 , π/2) concave upward concave downward

A trigonometric function of the form f(x) = a sin(x) + c has a maximum at 6.5 and a minimum at 2.5. The function would be: a) f(x) = sin(x) +9 b) f(x) = 9 sin(x) c) f(x) = 4.5 sin(2x) d) f(x) = 2 sin(x) + 4.5

Determine the length of the curve r = 4(1-sin(θ)). A) 32 units B 24 units C 36 units D) 30 units

Find the area of the region bounded by the curve r = a(1 - sinθ). (A) 3a²π (B) 32/3.a²π (C) 3/2a²π (D) 2a²π

Determine the length of curve r = a cos(θ). A) 3π/2 units B) aπ units C) 2aπ units D) π/2 units

Use the Law of Cosines to solve the triangle. Round your answers to two decimal places. B = 119° 30', a = 31, c = 31

Find and graph the odd and even part of the following signal. When A=5 g(t) = (n + 2t) Cos (2π/A t)

Write the expression in rectangular form, x + yi, and in exponential form, re^iθ [2(cos 3π/8+ i sin 3π/8)]^4 The rectangular form of the given expression is__and the exponential form of the given expression is.___ (Simplify your answers. Type exact answers, using as needed. Use integers or fractions for any numbers in the expressions.)

Because the values of circular functions repeat every 21, they are used to describe things that repeat periodically. For example, the maximum afternoon temperature in a given city might be modeled by the formula below. In the formula, t represents the maximum afternoon temperature in month x, with x = 0 representing January, x= 1 representing February, and so on. t=40-20 cos xπ/6 The maximum afternoon temperature in March is. (Round to the nearest integer as needed.)

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 = 49 sin s=

Find the exact values of s in the interval [0,2π) that satisfy the given condition sin^2 s= 3/4 s= (Use a comma to separate answers as needed. Simplify your answers. Type exact answers, using as needed. Use integers or fractions for any numbers in the expression.)

Solve the equation on the interval [0, 2π). 2 sin ^2θ-3 sinθ +1=0 What is the solution in the interval [0, 2π)? Select the correct choice and fill in any answer boxes in your choice below. A. θ= (Simplify your answer. Type an exact answer, using as needed. Type your answer in radians. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. There is no solution.

Solve the equation on the interval [0,2л). (tan θ-1)( cos θ + 1) = 0 Select the correct choice below and fill in any answer boxes in your choice. A. θ= (Simplify your answer. Type an exact answer, using as needed. Type your answer in radians. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. There is no solution on this interval.

Prove the identity (1/1-cosx) + (1/1+cosx) = 2csc^2x

x = sin θ cos θ and y = sin θ + cos θ are satisfied by which one of the following equations? (a) y² - 2x = 1 (b) y² + 2x = 1 (c) y² - 2x = -1 (d) y² + 2x = -1

Solve for x in the interval 0 ≤ x ≤ 2π 2 sin x +1 = csc x

The height of a rider on a Ferris wheel, in metres, can be modelled by the function; h(x)=9sin(x – 90)+10, where x is the rotation angle, in degrees, that you're on the ride. a. What is your maximum height on the Ferris wheel? b. What is your minimum height on the Ferris wheel? C. How far off the ground is the centre of the Ferris wheel? d. What is the radius of the Ferris wheel?