The double-angle identities are used when we want to simplify a trig expression. Similarly, you can use the half-angle identities to simplify trig expressions. These identities are also useful in engineering and physics concepts. sin(2a)=2sin(a)cos(a) cos(2a)=1-2sin^2(a) Use your knowledge of the half-angle and double-angle identities to simplify the following: (4sin(2a))-(2sin(2a))(4sin^2(a))

The double-angle identities are used when we want to simplify a trig expression. Similarly, you can use the half-angle identities to simplify trig expressions. These identities are also useful in engineering and physics concepts. sin(2a)=2sin(a)cos(a) cos(2a)=1-2sin^2(a) Use your knowledge of the half-angle and double-angle identities to simplify the following: (4sin(2a))-(2sin(2a))(4sin^2(a))

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.2: Trigonometric Functions Of Angles

Problem 2E

See similar textbooks

Related questions

Q: The sinusoidal function f(x)=48sin(6x−π9)+48 models the height, in centimeters, that a valve stem of…

A: The objective of this question is to find the time it takes for the valve stem of a tire to complete…

Q: Find the exact value of sin 2π sin ²-0 = 3 2π 3

Q: nd the coordinates of the trigonometric point associated with the real number ¹¹. 6 ive your answer…

Q: I don't understand this. This is for a practice guide, but I just don't understand this. Please type…

A: The objective of this question is to verify whether the given equation is a trigonometric identity.…

Q: The coordinates of a point P on the terminal arm of an angle are shown. What are the exact…

Q: Σ (1) sin( nul 150

A: 0\\ &2.\ b_{n+1} \leq b_n,\text{ for all n}\\ &3.\ \lim _{n \rightarrow \infty} b_n=0\\…

Q: The point A(given in the photo) is one of the vertices of a regular dodecagon inscribed in a circle…

A: Regular dodecagon has 12 equal edges. Internal angle at each vertex is 150∘.

Q: 2. Solve the equation tan² x + 2tanx - 3=0 for x, where 0≤x≤ 2π. ✓✓✓

Q: 1. Kelsi is running her horse again. Kelsi's horse starts running when it is due East of Kelsi and…

Q: A suspension bridge cable is constructed with an angle of elevation measuring (3pi)/8. If the…

A: A suspension bridge cable is constructed with an angle of elevation measuring (3pi)/8. If the…

Q: 4.) Given the vertical side is 9 m, and the horizontal side is 11 m, solve for the remaining sides…

A: Vertical side = 9 mHorizontal side = 11 m

Q: Let d be the distance in centimeters from the ceiling to the weight, when the weight is motionless,…

A: The objective of the question is to determine the midline, period, amplitude, and the maximum and…

Q: R 1 Find the interval, I, of convergence of the series. (Enter your answer using interval notation.)…

Q: Exercises Given that ∞ = - Given that. sin (2) 2 find cose secx, cScx cos (1) find sinx, tanx secx…

A: Note:-Since you asked multiple questions, according to our policy we can answer only first question…

Q: 1. Using these identities, prove the following: 1. Choose an angle between 61° and 89°. 2. Prove the…

A: Note:As per our guidelines we are supposed to answer only one question If there are multiple…

Q: Are the lines 3x-2y=3 and 6x-4y=10 parallel, perpendicular or neither? If applicable, find the point…

A: The parallel line do not intersect.If two line have the same slope, then the lines are parallel.

Q: Enter the number that belongs in the green box. [?] 59° 13

A: We know that the sines law states that,.Where a,b and c are the sides of triangle opposite to the…

Q: A с B b Ө с a For the diagram above, given that a= 2m and 8 = 50°, calculate the following: The…

A: need to find out the lengths of the sides AB and AC.

Q: solve sin(theta) - 1 = cos(theta) without using the double angle formula

A: To solve without using the double angle formula.

Q: Given sin t = -3/7

Q: Convert the given rectangular coordinates into polar coordinates. (1, -3)= ([?],[_]) Round your…

A: To convert the given rectangular coordinates into polar coordinates.

Q: Suppose the clock is resting on a table, the radius of the clock is 4 inches, and the hour hand is 3…

A: The objective of this question is to calculate the radian angle measure that the hour hand of a…

Q: Find tan x and sin xif secx = - and sin x > 0. 5

A: Given Trigonomteric Function are as follows this is only possible in first quadrant

Q: Find the values of x for which the series converges. (Enter your answer using interval notation.) 1…

A: The solution is given below

Q: 8. Which of the following values of x is NOT a solution of: tanx = 1? a) x == 7π 4 c) x = 5π 4 d) x…

A: The objective of this question is to find out which of the given values of x does not satisfy the…

Q: Let θ be an angle in quadrant I such that cosθ = 4/9 Find the exact values of cscθ and tanθ Let…

A: FINAL ANSWERS: Part Acsc(θ)=65965tan(θ)=465Part Bcos(θ)=−54csc(θ)=35tan(θ)=−43 Explanation:…

Q: Convert 23.98° to degree-minute-second form. If necessary, round your answer to the nearest…

A: The objective of this question is to convert a decimal degree measurement into degrees, minutes, and…

Q: Find the measure of each marked angle. The degree measure of the top angle of the triangle, with…

A: Given:A triangle with two interior angles and one exterior angle.To find:measure of each marked…

Q: 3. A Ferris wheel with a radius of 9.5 m rotates every 10 s. The bottom of the wheel is 1.2 m above…

A: To model the height of the rider on the Ferris wheel as a function of time, we can use a cosine…

Q: 3 33 -2 x dx

A: The given integral

Q: A deer runs 88 feet to the east, then turns and runs at an angle of 11° north of west for 127 feet.…

A: A deer runs 88 feet to the east, then turns and runs at an angle of 11north of west for 127 feet. To…

Q: Express the function h(x) = (x + 9) in the form fog. If f(x) = x, find the function g(x). Your…

A: Given that the function in the form fog ,and we have to find the function g(x)

Q: 5. Find the work (in J) done by a force F = 87 − 43+ 7k that moves an object from the point (0, 8,…

A: To find the work (in J) done by a force that moves an object from the point to the point along a…

Q: 7. Using a compound angle formula, determine the exact value for cos (12

Q: The bearing from A to C is S 61° E. The bearing from A to B is N 87° E. The bearing from B to C is S…

A: The figure

Q: 30 Given 0-72", and the opposite side is 4 yards long, solve for the remaining sides and angles.

A: Given:angle opposite side = 4 yardsTo find:remaining sides and anglesSum of angles of triangle =

Q: Graph the function for -π≤theta≤2π. How is the graph related to the graph of y=tan theta? g(theta)=2…

A: The objective of this question is to graph the function g(theta) = 2 * tan(theta) for -π

Q: 2. Farmer John has land on both sides of a river as shown in the diagram below. He wants to build a…

A: We need to find the length of cable required and the cost.

Q: Use the Law of Cosines to solve. 6. Two flying drones leave an airport at the same time. The heading…

A: The figure with given information

Q: Find the slope of the line passing through the origin which satisfies the given additional…

A: The line is perpendicular to a second line. passing through the origin at an angle of 5π / 8

Q: Find tan 345° without using a calculator. Sum & Difference Formula Tangent tan(A + B) = _tan A ± tan…

Q: Let theta be an angle in first quadrant with cos=a. Evaluate the following in terms of a. Cos…

A: The objective of the question is to find the value of Cos (theta + 360°) in terms of 'a' when cos…

Q: A lamppost cast a shadow of 12 ft when the angle of elevation of the Sun is 33.8°. How high is the…

A: A lamppost cast a shadow of 12 ft when the angle of elevation of the Sun is 33.8°. How high is the…

Q: Find all values of 0 if 0 is in the interval [0°,360°) and has the given function value. tan 0…

A: Given Trigonometric function is as follows

Q: Simplify. tan(-x) cos(-x)

A: Given in this questionusing the formulas

Q: It should be a -c at the end for the start of the equation.

A: By using the Law of Cosines to prove that, .

Q: A plane flies 110 miles per hour for 1 hour on a bearing of 040. From that point, it then turns and…

A: The figure

Q: Find the area of this triangle. 32 48 63 [? ]ft² Round to the nearest whole number.

Q: Determine the exact value of 2 cos² (75⁰) – 1

Q: 17.6 50°

A: Let the h be the height of the cactus The figure

Question

You learned the double angle identities in the lesson content. The double-angle identities are used when we want to simplify a trig expression. Similarly, you can use the half-angle identities to simplify trig expressions. These identities are also useful in engineering and physics concepts. sin(2a)=2sin(a)cos(a)

cos(2a)=1-2sin^2(a)

Use your knowledge of the half-angle and double-angle identities to simplify the following:

(4sin(2a))-(2sin(2a))(4sin^2(a))

Figure in plane geometry formed by two rays or lines that share a common endpoint, called the vertex. The angle is measured in degrees using a protractor. The different types of angles are acute, obtuse, right, straight, and reflex.

Expert Solution