The area A of a triangle with sides of lengths a and benclosing an angle of measure u isA = 1/2 ab sin θ. How is dA/dt related to du/dt, da/dt, and db/dt if none of a,b, and θ are constant?

Q: 2. Identify each of the following polar equations and state the correct graph: a. r 2-2 cos 0 i. ii.…

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Q: Find sin a. (-3, 4) sin a = [? r

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Q: show that r = cos 2θ is symmetrical with respect to the horizontal axis.

A: show that r = cos 2θ is symmetrical with respect to the horizontal axis.

Q: points

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Q: t Angle x lies in the 4th quadrant and tan x : 7 Angle y lies in the 2nd quadrant and 24 40 siny…

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Q: TC 4. Give the exact value of sin (- 12

A: The given trigonometry ratios is sinπ12

Q: Let be the angle between u and v. Find cos(0). cos(0) = u = [6, 5, -1], v = [1,-1, 1] Determine…

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Q: C 25 7 T

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Q: If possible, evaluate the following. If not, state why the expression cannot be eva Hint: Draw a…

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Q: 4. Solve for the area common with r = 2+5 cos(20) and r = 5 sin(0).

A: Solve for the area common with r=2+5cos2θ and r=5sinθ.

Q: Convert r=1/1+sinθ to Cartisian

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: 1. If tan⁡θ=3/4 and θ is in QIII, what is csc ⁡θ? 2.  3.

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Q: cos a Jsin a

A: Given: ∫cos5αsinαdα =∫(1-sin2α)2cosαsinαdαApply u-substitution u=sinα…

Q: F k d

A: Use conic section we can prove it.

Q: 1. Fig.1 is a part of a spherical shell. It may be described as 3≤r ≤5, 40°≤0 ≤90°, 20° °<50° where…

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Q: Computation for the points and area of intersection of r = 2 and r = 3 − 2 cosΘ

A: Equating r=2 and r=3-2cosθ to find point of intersection, we get 3-2cosθ=2⇒2cosθ=1⇒cosθ=12⇒θ=π3, 5π3…

Q: 6. Plot r = 4 cos O :

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Q: he = = = du 00 r cos 0 cos oT + r cos sin ój-r sin OF or

A: hθ=|rcosθcosϕi+rcosθsinϕj-rsinθk|

Q: b=2 and sin v= 5/17. evaluate a

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Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.