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# Trigonometry

### Mathematics - Trigonometry - Identities

Prove the following Identities: Prove the following Identities: 1. tan² A / sec² A = 1 - cot ² A / csc² a 2. 1 / 1 - cos A tan A = cot A / cot A - cos A 3. cos² A ( 1 - sec² A) / cot² A sin² A - 1 = 1 4. (cot A = tan A) ² = sec² B csc² B°

### Fundamental Identities - Single trigonometric function

Simplify to a single trigonometric function: 1. 1 / tan A csc A = 2. sin² A cot A / tan A = 3. tan A cot A + 1 / cos A = 4. sin² A sec² A / cos A csc A =

### Trigonometric identities found

Prove the following Identities: 1. sec A = cos A (tan² A + 1) 2. sec² A = sin² A + cos² A + tan² A 3. 1 + sin A = cos² A / 1 - sin A 4. cot A csc A / sec A = cot² A + 1 / tan² A + 1

### Bearings/Courses - 1. A car traveling due west is sighted 2 km directly north of a radar outpost. 10 minutes later, its bearing is N 78° 30' W. find the speed of the car per hour.2. A boat is 25 km due west of a lighthouse A and lighthouse B is 15 km due north of lighthouse A. find the distance LH B to the boat and the bearing of LH B from the boat.

1. A car traveling due west is sighted 2 km directly north of a radar outpost. 10 minutes later, its bearing is N 78° 30' W. find the speed of the car per hour. 2. A boat is 25 km due west of a lighthouse A and lighthouse B is 15 km due north of lighthouse A. find the distance LH B to the boat and the bearing of LH B from th

### Trigonometric Identities

ASSIGNMENT 6 7.4 Use an identity to write each expression as a single trig function value or as a single number. 14. 1 - 2 sin square 22 ½ degree Express as a trig function of x 22. sin 4x Write each expression as a sum or difference 44. sin 4x sin 5x Write each expression as a product 46. cos 5x + cos 8x

### Trigonometry questions

See attached ASSIGNMENT 5 7.1 2. if cos x = -.65, then cos (-x) = -.65 Find the remaining five trig functions of theta 22. cos theta = 1/5, theta in quadrant I 30. tan x = D sin x/cos x T or F 34. - tan x cos x = Write each expression in terms of sine and cosine and simplify 52. cot square theta

### Trignometry: Right triangle applications

1. A closed-circuit camera is mounted on a 7.5 feet wall above a security desk. if it is used to view an entrance door 9.5 feet away from the desk. find the angle of depression from the camera lens to the entrance door. 2. The angle of depression from a search light to its target is 58°. How long is the beam of light if the

### Inverse Trigonometric Functions - Evaluate Inverse

Evaluate the ff. inverse trigonometric expressions 1. cot (arcos 0.6729) 2. sin (arctan 5.2913) 3. cot (arctan 3.9127) 4. tan (arcsin 0.9315) 5. tan (arccot 0.7381)

### Inverse Trigonometric Functions

Evaluate the ff. inverse trigonometric expressions: 1. arctan [ cos (arcsin 0.75) ] 2. cos [ arcsin (cot &#960; / 3) ] 3. arcsin [ cos (arccos 0.5) ] 4. sec (arcsin &#8730;3 / 2) 5. cos (arcsin 1 / &#8730;2)

### Inverse Trigonometric Function

Evaluate the following inverse trigonometric expressions: 1. sec (3 arctan 3/4) 2. sin (4 arccos 1/2) 3. cos (2 arcsin 3/7) 4. cos (3 arccos 2/3)

### Triangles used in solving word problems

1. Anne is pulling on a 60 foot rope attached to the top of a 48-foot tree while Walter is cutting the tree at its base. How far from the base of the tree is Anne standing. ( picture a triangle with the hypotenuse is 60 ft. and the back of the triangle is 48 ft from top to the base x ft. ) (the back is the right side and the h

### Location and Reference Angle of Trigonometric Function

Indicate the quadrant location of the angle, the algebraic sign, reference angle and numerical value. 1. csc -( 7pi / 3) 2. cos ( -2,192°) 3. tan ( 1,178°) 4. sin ( 39pi / 11)

### Finding Quadrant and Sign of a Trigonometric Function

Find the quadrant of the angle, sign, reference angle and value of the trigonometric functions below: 1. sin 642° 2. csc ( -8.785) 3. sec ( 23pi / 5 ) 4. tan ( -7.228)

### Trigonometry Algebra Equations

A single question on trigonometry. An example is provided of a similar question. Please provide it to the same level of detail. Find sin^5*theta and cos^5* in terms of sin n*theta and cos n*theta

### trigonometric Functions of Quadrantal Angles

Evaluate the following expressions involving quadrantal angles: 1. sin180°cos180°- 3cos540°cos720° = ?

### evaluate trigonometric expression

How do I evaluate the following trigonometric expression involving special angles? 1. sin60° cos30° - cos45° sin45° 2. tan60° - tan45° / 1 + tan60° tan45° 3. [1 + cot² 30°]³ Please explain.

### Complete solution

Find the complete solution of...

### Trigonometry Plan Questions

A) Give the vale of : (i) sin^-1 (cosx ), only acute angle. (ii) tan (sin^1 x) (iii) tan [ tan^-1 ( x+ 1)/(x-1) + tan ^-1 (x-1 )/x b) Solve : cos^-1 x + cos^-1 2x = 60° c)State what is the most interesting thing learnt in studying Trigonometry and why you have select it to be introduced in your

### Solve Trigonometry - Based Proof

Question: a) Prove that tan 15degrees = 2 - sqrt(3). b) Solve, for 0 </= theta < 360 degrees, sin (theta + 60 degrees)sin (theta - 60 degrees) = (1 - sqrt(3)) cos^2(theta)

### Important information about solving trigonometric equation

I need check about these : A) Solve the following, giving all positive values of the angle between 0° and 360° to the nearest minute only. i) cos2x-sin^2 (x/2)+3/4 = 0 ii) cos4x =sin2x iii) sin^2 theta = cos^2 theta +3/2 iv) sin(2x-10°)= 1/2 v) sin2x-cosx = 0 b) Write equivalent equations in the form of inverse

### Plane Trigonometry - A) Solve the following, giving all positive values of the angle between 0° and 360° to the nearest minute only ...

A) Solve the following, giving all positive values of the angle between 0° and 360° to the nearest minute only. i) cos2x-sin^2 (x/2)+3/4 = 0 ii) .cos4x =sin2x iii)sin^2 theta = cos^2 theta +3/2 iv)sin(2x-10°)= 1/2 v) sin2x-cosx = 0 B)Write equivalent equations in the form of inverse functions for : a)x= y+costhet

### Applications of the Pythagorean Theorem

Measure the height of your computer monitor to the nearest tenth of a centimeter or sixteenth of an inch. Measure the width of your monitor as well. Use the Pythagorean theorem to find the length of the diagonal of your monitor. In your post, include the height, the width, and the calculations needed to determine the length o

### Views of God in Ancient Philosophy

Is there a God according to ancient philosophy?

### Plane Trigonometry: Verifying Identities

1) Verify the following identities : a) sin(x+y)cos(x-y) + cos(x+y)sin ( x-y) = sin 2x b) cos2x = [cot^2 (x-1 )] / [ cot^2 (x+1) ] 2) Derive the identity for sin 3x in terms of sin x 3) Using the double-angle formula, find sin 120° . 4)Simplify the following expressions so that they involve a function of only on

### Using Logarithms to Find the Area of Triangles

1) Using logarithms find the area of the following triangles : i) a = 12.7, b = 21.5,and c = 28.6 ii) c = 426, A= 45° 48' 36", and B = 61° 2' 13" iii) An isosceles triangle in which each of the equal sides is 14.72 in. and the vertex angle 47° 28' . 2) Find the radius of the inscribed circle and the radius of

### Solve the Antiderivative Problem

Need help with the steps to solve and antiderivative problem with some trig functions. I believe the trig is what is messing me up. See the attached file.

### Application of Trigonometry for Surveying

To determine the distance to an oil platform in the Pacific Ocean from both ends of a beach, a surveyor measurers the angle to the platform from each end of the beach. The angle made with the shoreline from one end of the beach is 83 degrees, from the other end 78.6 degrees. If the beach is 950 yards long, what are the distances

### Periodic Functions

Please see the attached file. Many periodic functions do not have a period of 2pi. One example is the function g(t) shown below...

### Wheelchair Ramp and Trigonometry

A contractor is building a wheelchair accessibility ramp (see figure attached) for a business. Using your knowledge of right-triangle trigonometry, help advise him how to create a ramp whose dimensions will meet the specification needed that will allow wheelchair accessibility. Talk about the procedure the contractor will need t

### Unit - 5 Individual Project (B)1

Unit 5 Individual Project - B [See the Attached Questions File.] 1. The following chart shows some common angles with their degrees and radian measures. Fill in the missing blanks by using the conversions between radians and degrees to find your solutions. Show all work to receive full credit. 2. Two boats leave the port a