The following identities are from the book Plane and Spherical Trigonometry with Tablesby Rosenbach, Whitman, and Moskovitz, published by Ginn and Company in 1937. Verifyeach identity.  (tan theta +cot theta )2 = sec2 theta+ csc 2  theta

Q: Use the information given about the angle θ,0 ≤ θ <2π, to find the exact value of (a) sin( 2θ )…

A: Consider the given equation as tanθ=12

Q: ABC is a right angled triangle with AB = 4 units and BC = 3 units Prove that for the angle marked x°…

A:

Q: In each of the following cases, sketch and label an angle 0 in the Cartesian plane that is in…

A: "Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Find the area of the sector formed by the given central angle  theta in a circle of radius r.…

A: From the given data: r=5 cm Theta= 3

Q: Use the unit circle to find the exact value of the stated functio cot 2π B) Undefined 2√3 D) 0 3 A)…

A: Given query is to find the value of indicated function.

Q: In the triangle ABC, the altitude through A, the median Question 2 through B and the internal angle…

A:

Q: Use the information given about the angle θ,0 ≤ θ <2π, to find the exact value of (a) sin( 2θ )…

A: Consider the trigonometric ratio, tanθ=-3, 0≤θ≤2π Use the information given about the angle θ,…

Q: - In the acute- angled triangle OPQ, the altitude OR makes angles A and B with OP and OQ. Show by…

A:

Q: Find the area of the sector formed by the given central angle  theta in a circle of radius r.…

A: Given that θ=2.4,r=4 inches.

Q: Find the area of the sector formed by the given central angle theta in a circle of radius r.…

A: Given that θ=75°,r=10m. First change the angle in radians. θ=75×π180=5π12

Q: Use the drawing provided to show that the area of the isosceles triangle is A = s? sin 0 cos 0. S…

A: From the triangle, using the trigonometric ratio, sinθ=xsx=ssinθ and, cosθ=ysy=scosθ

Q: Suppose that 0 is an angle in standard position whose terminal side intersects the unit circle at 20…

A: Intersection point is -2029,2129.

Q: Draw an angle with a measure of theta that satisfies both conditions, a) cos theta is negative b)…

A:

Q: Express the circle specified by ?=2cos(?)?=1+2sin(?) y=1+2 sin(?) inin Cartesian coordinates and…

A: Equation of a circle with radius r and center (h,k) is  (x-h)^2 + (y-k)^2  = r^2

Q: So A = 2m %3D 2.

A: Here it is given that θ is the radian measure of a central angle of a circle and r is the radius of…

Q: 12 Given that cot(0) = = and 0 is in Quadrant III, find sec(0) and csc(0). %3D

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Q: Consider the friangle AFSU below. S 143 55 F U 132 Using what you know about trigonometric…

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Q: Given that cos 0 12 %3D 13 and that angle 0 terminates in quadrant IV, then what is the value of sin…

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Q: Consider the length h of the perpendicular from point B to side b in the given triangle. Show that b…

A: From the given figure, let the perpendicular from point B meets the side AC at D.

Q: On a circle with radius of 10 cm, find the length of the arc that subtends the central angle of 72.…

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Q: Use the information given about the angle θ,0 ≤ θ <2π, to find the exact value of (a) sin( 2θ )…

A: We have given   sinθ=-33 and 3π2<θ<2π cosθ=1-sin2θ=1--332=1-13=23 cosθ will be positive since…

Q: Use the following triangle to find sec 0. V74 NOTE: Enter the exact, fully simplified and…

A: Solve the following

Q: 9. 13D 10. If OM = 12, what is G F I C. J D E 1. Name four radii of circle C. 2. Name a diameter of…

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Q: 5. For the right triangle below, what are (a) the length of the unknown side, (b) the tangent of 0…

A: Given,            The right triangle is shown below :

Q: Suppose that 0 is an angle in standard position whose terminal side intersects the unit circle at 7…

A: Solution: The objective is to find the required values

Q: In the triangle show below sec 0 is A В

A: Solution:-

Q: that follow. Use separate paper. J 1. Radius 2. A diameter 3. A chord 4. A semi -circle 5. A minor…

A: Given the circle is

Q: Use the information given about the angle θ,0 ≤ θ <2π, to find the exact value of (a) sin( 2θ )…

A: If an angle lies in the first quadrant then all trigonometric functions of that angle are…

Q: the law of sine for plane triangles given by All of the above is true .I O sina/a sine/b sinø/c .I O…

A: In this question we have to choose the law of sine of plane triangles

Q: of the negida cut from the first aree 2- Find the quadrant by the regiön r= I+Sin@ ?

A:

Q: Find the area of a sector of a circle having radius r and central angle 0. If necessary, express the…

A: The Area of a sector of a circle having the radius r and central angle θ is expressed as :…

Q: Find the area of the sector formed by the given central angle  theta in a circle of radius r.…

A:

Q: Given that cos(0): V17 and 0 is in Quadrant III, what is sin(0)? %3D 17

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Q: Prove that if r - Geom (p), then E (x²)

A: Here, X~Geom(p).

Q: Find the area of the sector formed by the given central angle  theta in a circle of radius r.…

A: Given: θ=2π5, r=3m

Q: Find the area of the sector formed by the given central angle  theta in a circle of radius r.…

A: To find the area of the sector formed by the given central angle θ=2 in a circle of radius r=3 cm.

Q: Refer to the figure below showing a point P(x, y) on the terminal side of an angle A. P(x, y) -6 -5…

A:

Q: Which of the following is the area of the sector whose radius is 1.4 miles and a central angle of…

A: We know that, Area of a sector = θ360πr2

Q: In each of the following cases, sketch and label an angle 0 in the Cartesian plane that is in…

A: Explanation of the answer is as follows

Q: The following triangle can best be classified as: O both equilateral and equiangular O equilateral O…

A:

Q: Explain the following “proof without words” of the law of cosines. (Source: Kung, Sidney H., “Proof…

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Q: Consider the given figure. B What information about this figure would be used as a step in a proof…

A: In the given figure, it is already clear that CD is the  perpendicular bisector of AB. Showing that…

Q: se the Law of Sines to verify that there is no such triangle that satisfies the given conditions: =…

A:

Q: 8 find the following. 15 13 If a and B are acute angles such that csc a = – and cot B = %3D 12 (a)…

A: Given: csc α=1312we know, csc α=1sin α  sin α=1213     so

Q: Consider the following triangle: 15 Give the exact values of the following (decimal approximations…

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Q: Consider the two unit circles below. From the information provided in both diagrams, find the…

A: Concept: Trigonometric ratios: sinθ=PH cosθ=BHtanθ=PB Where P is the perpendicular, B is the base…

Q: The following problem refers to right triangle ABC with C = 90°. Use the given information to find…

A: A right triangle ABC with C = 90o b = 10, c = 26 We need to find the six trigonometric functions of…

Q: Consider the length h of the perpendicular from point B to side b in the given triangle. Show that

A: The triangle ABC is  We have to prove   ,where  the length h of the perpendicular from point B to…

Q: the law of sine for plane triangles given by All of the above is true I O sina/a sine/b sino/c O II…

A: sine rule for triangles is asinα=bsinθ=csin∅

Q: Let ZD be an acute angle such that cos D = 0.33 . Use a calculator to approximate the measure of ZD…

A: For a angle ∠D, if given cos D=a⇒D=cos-1a, where -1≤a≤1

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.