### Convert a cis θ (cos θ + i sin θ) expression into trigonometric form.

Please see the attached file for the fully formatted problems.

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Please see the attached file for the fully formatted problems.

If a and b are acute angles with Sin a =2/5squared and b = 1/5 squared, find the exact value of sin (a + b)

1.) A fugitive is running along a wall at 4.0m/s. A searchlight 20m from the wall is trained on him. How fast is the searchlight rotating at the instant when he is 10m from the point on the wall nearest the searching? 2.) A balloon is rising from the ground at the rate of 6.0m/s from a point 100m from an observer, also on the

Prove that sin2 x + cos2 x = 1 using only this information : Cos x = (e^jx + e^-jx)/2, sin x = (e^jx - e^-jx)/(2j) See attached file for full problem description.

A nautical mile depends on latitude. It is defined as length of a minute of arc of the earth's radius. The formula is N(P) = 6066 - 31 cos 2P, where P is the latitude in degrees. a) Find the exact latitude (to 4 decimal places) of where you live, used to live, work, or used to work (include the zip code). The latitude fo

Please see the attached file for all of the fully formatted problems. 1. You have calibrated your voltmeter so that you know a meter reading of 10 V is actually 10.2 V and a reading of 15 V is actually 15.6 V. What is the actual voltage when your meter reads 12.3 V? (1) 11.9V (3) 12.3 V (5) 13.1 V (2) 12.1 V (4) 12.7 V (6

(a) Sketch the graph of y = cos X in the range - π ≤ X ≤ π. π="pi" Hence sketch the graph of y = cos X in the same range. (b) Find the mean value of y = cos X in the range - π ≤ X ≤ π

What is the length of the diagonal of a rectangular billboard whose sides are 5 meters and 12 meters? keywords: hypotenuse, Pythagorean

Suppose at kickoff of a football game, the receiver catches the football at the left side of the goal line and runs for a touchdown diagonally across the field. How many yards would he run? (A football field is 100 yards long and 160 feet wide).

#120 Digging up the street. A contractor wants to install a pipeline connecting point A with point C on opposite sides of a road. To save money, the contractor has decided to lay the pipe to point B and then under the road to point C. Find the measure of the angle marked x in the figure for exercise #120 on page 161.

Use trigonometric identities to factor and simplify the following: ? sin^2 x * sec^2 x - sin^2 x

Match sin x sec x with one of the following: ? csc x ? tan x ? sin x tan x ? sin x cot x Use trigonometric identities to factor and simplify the following: ? sin2 x * sec2 x - sin2 x

Which one of the following trigonometric functions of x is not correct? Which one of the following trigonometric functions of x is not correct given that sin x > 0 and sec x = -2? ? csc x = ( 2 sq rt 3) / 3 ? cos x = - 1 / 2 ? cot x = - ( sq rt 3 ) / 3 ? tan x = - ( sq rt 3 ) / 2

Match sec4 y - tan4 y to one of the following: ? csc y ? sec2 y+ tan2 y ? 1+ tan y ? csc y x cot y

Prove the identity of this problem. sin x - sin y x - y -------------- = tan (--------) cos x - cos y 2 keywords : find, finding, calculating, calculate, determine, determining, verify, verifying, evaluate, evaluating, calculate, calculating, prove, proving

Here is an example of the problem that I am working on at this time. I need to know how to list the transformation needed to change the graph of f(t) into the graph of g(t). f(x) = sin t; g(t)= -3 sin t

Solve each equation for solutions over the interval [0,2π) sin x + 2 = 3 2 sec x + 1 = sec x + 3 Solve each eqation for solutions over the interval [0º,360º) cos²Θ = sin²Θ + 1 4cos²Θ + 4cosΘ = 1 See attached file for full problem description.

For the following trigonometric equation, find all solutions in the interval 0≤ θ ≤ 360 2 cot θ sec θ = 3

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 Θ that makes each statement true Find cos(s+t) and cos(s-t) Please see the attached file for the fully formatted problems

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

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

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

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

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

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

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

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

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

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

Write -8 - 8j in a trigonometric form