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# Trigonometry

### Solving Trigonometric Equations

For the following trigonometric equation, find all solutions in the interval 0&#8804; &#952; &#8804; 360 2 cot &#952; sec &#952; = 3

### Trigonometric Identities and Cofunctions of Complementary Angles

Find sin s Cot s = -1 / 3, s in quadrant IV Verify each trigoometric equation is an identity Write each function value in terms of the cofunction of a complementary angle. Find an angle &#920; that makes each statement true Find cos(s+t) and cos(s-t) Please see the attached file for the fully formatted problems

### Trigonometry : Solving Identites Over Given Intervals

Solve the following equations in the interval given in brackets: &#8730;3 sin 2θ + 2 sin^2 θ=1 {0 ≤ θ ≤ pi} cos 2θ=5 sinθ {-pi ≤ 0 ≤ pi}.

### Solving a Tangent Function using Trigonometric Identities

Tan (a + b) = (5/12 -1/sqrt3) / 1 - (5/12)(-1/sqrt3)

### Relations Including the Trigonometric Functions

1. Prove that cotx/(1+tan(-x)) + tanx/(1+cot(-x)) = cotx+tanx+1 2. Prove that (sinx+tanx)/(1+secx) = sinx.

### Solving Trigonometric Identities on an Interval

Find all solutions in the interval [0,2pi): cos2x + 5cosx = 2

### Solving Trigonometric Equations over an Interval

Find all solutions in the interval [0,2pi) A) cos3x + 7cosx = 3 B) 4sin^2x + 9sinx + 7 = 0

### Proving Identities

We have been working on proving identities and it's a subject I just can't get my brain around. A few of the problems we've been given have made me stumble. cotx/1+tan(-x) + tanx/1+cot(-x) = cotx + tanx +1 I figure on this one, with using identities, I can get: cotx/1-tanx + tanx/1-cotx = cotx + tanx +1 But I can't g

### Finding the Sine of an Angle

In a right triangle, use standard labeling, you are given a=3.27, b=7.84, c=8.49, find sin A.

### Trigonometry : Graphs, Asymptotes and Phase Shifts (13 Problems)

1. If sin(alpha)=1/5 where alpha is in quadrant II, find the remaining five trigonometric functions of alpha. 2. Given that sin(alpha)= -2/3 and cos(alpha)= -root5/3>0, find the remaining four trigonometric functions. 3. Sketch a graph of y=3cos(2theta+pi) using either transformations or the "5 key points" method. Be

### Applying Trigonometric Identities

Which of the following is identical to cos 5x cos 3x + sin 3x sin 5x? cos 2x cos 8x sin 2x sin 8x

### Trigonometric Identities Functions

Which of the following is identical to sin^2 3x+ cos^2 3x 6 18 1 3

### Cosine Relations

Which of the following is identical to cos(x+(Pi/2))? -sin x sin x sinx+cosx cos x.

### Trig questions; graph of tangent, latitude/nautical mile, polar coordinates

Please explain and show all of your work For number 2 please use any address and zipcode for Chicago or a suburb of Chicago. Please show the address and zipcode as well. 1. Consider the graph of y = tan x. (a) How does it show that the tangent of 90 degrees is undefined? (b) What are other undefined x values? (c) What is

### Verifiying Trigonometric Identities

Verify the identity algebraically: 1+ cos 10y = 2 cos^2 5y

### Solving Trigonometric Equations Intervals

Approximate the solution of the equation in the interval [0,2pi]. If possible find the exact solutions algebraically. (sin 2x + cos 2x)^2 = 1

### Solving Trigonometric Equations in a Quadrant

Suppose cos(u) =-6/7 and sin(v) =3/4. If u and v are in quadrant 2, find cos (u+v)

### Solving Trigonometric Equations

Find all of the exact solutions for the equation: 3-3sin(x)=2cos^2(x)

### Solving Trigonometric Identities

Prove the trigonometric identity 1 + cosx = 1 _______ _________ sinx cscx - cotx

### Adding Vectors using Trigonometry

Given vectors v= 150mi at 175 degree and w= 270 mi at 215 degree. Find the sum of v and w.

### Trigonometry Word Problems

A tree casts a shadow 86 ft long when the angle of elevation of the sun is 48.7 degrees. Find the height of the tree.

### Trigonometry Word Problems

Find the angle of elevation of the sun at the time when a 25 foot tall tree casts a 40 foot long shadow.

### Trigonometry Word Problems Presented

From a boat sailing due north at 16.5 mph a wrecked ship K and an observation tower T are observed in a line due East. One hour later the bearings from the boat to K and T are S34(deg)East and S65(deg)East, respectively. Find the distance between K and T. keywords: bearings

### Trigonometry Word Problems For Travel Directions

A boat travels in a direction of N40(deg) E for 3 hours at 20 mph. How far North and how far East did the boat travel? keywords: bearings

### Trigonometry Word Problems (Trapezoids)

See attached file for full problem description. Please show answers with all steps.

### Completing Trigonometric Identities

Complete the Identity: 1. cos 4(theta) 2. sin(theta) sin(theta) ---------- - ---------- 1+sin(theta) 1-sin(theta) Use the given information to find the exact value of the expression. 3. Find sin(2theta). tan(theta) = 24/7, theta lies in quadrant III.

### Trigonometry Word Problems for a Surveyor

1. A surveyor is measuring the distance across a small lake. He has set up his transit on one side of the lake 130 feet from a piling that is directly across from a pier on the other side of the lake. From his transit, the angle between the piling and the pier is 55(degrees). What is the distance between the piling and the p

### Derivatives of Inverse Trigonometric Functions

Y = ln(t^2 + 4) - 1/2 arctan t/2

### Using Trigonometry Identities

What are different kinds of trig identities? Questions: 1. If sin x = -1/3, what is cosx? 2. Simplify the expression (sinx + cosx)^2 + (sinx - cosx)^2 3. Verify the identity cotx - tanx = (csc2x - sec2x)/sinxcosx

### HOW FAR IS THE FIRE FROM B?

LOOKOUT STATION A is 15 km west of station B. THE BEARING FROM A TO A FIRE DIRECTLY SOUTH OF B IS 37 DEGREES AND 50'E. HOW FAR IS THE FIRE FROM B?