If A, B and C are angles of a triangle, prove that sin A = sin (B + C) and hence that          sin A – sin (B – C) = 2 cos B sin C.

Q: If v x w = (-1, 4, 0) and v · w = 4, find tan(0), where 0 is the angle between v and w. tan(0) =

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

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Q: assume that all the given angles are in simplest form, so that if A is in QIV you may assume that…

A: Given  where A is in quadrant II

Q: solve for the angle u, where 0 … u … 2π cos 2θ + cosθ = 0

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Q: Suppose v. w = 6 and ||7× w|| = 4, and the angle between ỹ and w is 0. Find (a) tan 0 = (b) Ө —

A: v · w= |v| × |w| × cos(θ) =6 v × w = |v| |w| sin(θ) =4

Q: If w=f(a,b,c)=cos(ab)sin(b)+c, what is at ( 2'3 5,6 )?

A: Given function is  w=fa,b,c=cos(ab)sin(b)+c

Q: If sin D = cos E, then z D and z E must be angles. 7. O A adjacent B. complementary C. congruent O…

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Q: Suppose v w = 5 and ||0 x w 3, and the angle between õ and w is 0. Find (a) tan 0 %3D (b) 0 = (in…

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Q: If A, B, and C are the angles in a triangle, show that sin 2A +sin 2B +sin 2C = 4 sin A sin B sin C

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Q: assume that all given angles are in simplest form, so that if A is in QIV you may asssume that 270o…

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Q: Find

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Q: If A,B and C are interior angles of a triangle ABC , then show that sin(B+C/2) = (cosA/2)

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Q: Assume that is a positive acute angle. Given: sin = Find: sin 20 24 25

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Q: If i x w = 3i+ 2j – between i and w, then k, and i· w = 4, and 0 is the angle (a) tan 0 (b) 0 : ||

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Q: Use the given conditions to find the exact values of sin(2u), cos(2u), and tan(2u) using the…

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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: Find the angle 0 between w = cos 플 i+ sin푸 7 cos플 i + sin and %3D

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Q: Show that, given the three angles A, B, C of a triangle and one side, say a, the area of the…

A: Let's add a draw a diagram to help us out.   The area of any triangle is given by                A =…

Q: Use the given conditions to find the exact values of sin(2u), cos(2u), and tan(2u) using the…

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Q: If the angle & (measured in radians) is such that 21 << ST 2 a) cos x < -√2 < sin x 2 b) √2 < cos…

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Q: Let sin(30°) Enter an angle measure (3), in degrees, for cos(B) 1/2

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Q: Find the angle between u=⟨4​,−1⟩ and v=⟨5​,−4⟩ to the nearest tenth of a degree

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Q: In any triangle ABC, prove that sin A sin B sin C 3 sin B+ sin C sin C+ sin A sin A+ sin B 2.

A: Consider the left side of the given equation, sinAsinB+sinC+sinBsinC+sinA+sinCsinA+sinB

Q: Consider two angles A and B on a standard coordinate plane such that: 4 3 sin(A) 5 cos(A) 5 40…

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Q: Let a be angle such that cos a = -- and sin a > 0. What is the exact value of sin a?

A: Only 2nd quadrant is the only region where cosα is -ve and sinα is +ve

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: Show that if tan0 = c and 0 &lt; 0 &lt; π/2, then cos0 = 1/ 1 + c2.Hint: Draw a right triangle whose…

A: tan θ=cTo find: Value of cosθ, where 0≤θ≤π2

Q: 25x Using the compound angle formulae equals sin 12 a) sin 3 O b) sin 3 c) sin 3 4 O d) sin +-

A: Sin(25π/12) = Sin(2π + π/12) = Sin(π/12)

Q: Suppose that a and ß are in the first quadrant, sin(a) = , and sin(B) = . What is sin(a + B)?

A: cos2α=1-sin2α sinα+β=sinαcosβ+cosαsinβ

Q: If sin D cos E, then 2D and ZE must be angles. %3D A adjacent A. complementary B. C. congruent…

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Q: Suppose - w = 5 and ||i x u|| = 2, and the angle between i and w is 0. Find %3| (a) tan 0 (b) e

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Q: Given that sin(theta) > 0 and sec(theta) > 0 , in which quadrant does

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Q: If a,ß are acute angles such 8 4 and tan ß =, find 5 that cos a = a. cos(a-ß) a b. sin 2

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Q: 6. If A,B and C are interior angles of a triangle ABC, then show that B+C sin A = cos

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Q: Suppose 0 is an angle such that cos(0) %3D 3 If 0 < 0 < T, then cos and sin 2 If T < 0 < 27T, then…

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Q: Explain why there is no angle ? such that sin theta= 2.  If sin theta= y/r = 2, then y would have…

A: We will use polar co-ordinates to solve this

Q: 4. Find the angle between w = –3i + V33 and =

A: Angle between two vectors is given by,

Q: ; Suppose v · w = 8 and ||3 x w|| = 2, and the angle between v and w is 0. Find (a) tan 0 (b) 0 =

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Q: Let v = -5i + 2j and w = 2i - 4j. Find the angle between v and w, to the nearest degree.

A: Given, v=-5i+2jw=2i-4j

Q: Consider angles A, B, and C such that cos A = cos 217°, tan B = tan 298°, sin C = sin 7 where 0° A≤…

A: Here we have cosA=cos217°, tanB=tan298° and sinC=sin7° Here 0°≤A≤360°, 0°≤B≤360°,0°≤C≤360°. Suppose…

Q: In any triangle ABC prove that a sin (B-C) + b sin ( C - A) + c sin ( A - B) = 0

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Q: In right ∆QRS, Angles Q and R are the acute angles. If tan Q = √51/7, determine cos R.

A: We have used the Pythagoras Theorem in this question.

Q: Use a coterminal angle to find the exact value of the exgression. De nt sin 750° O 2 O 23 3. 1/2

A: Given:   sin(750°)writing 750°=2×360°+30° sin(750°)= sin(2×360°+30°)we know that 360°=2πThen…

Q: In any triangle ABC, prove that a sin (B – C) + b sin (C – A) + c sin (A – B) = 0.

A: In any triangle ABC, prove that a sin (B – C) + b sin (C – A) + c sin (A – B) = 0

Q: If A(a, b), B(a + r cos 0 , b + r sin 0) and C(a +r cos B,b +r sin ß) are the corner points…

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Q: Use the given conditions to find the exact values of sin(2u), cos(2u), and tan(2u) using the…

A: Given , sinu=-45,3π2&lt;u&lt;2πIn 3π2&lt;u&lt;2π , cosu is positivethen by pythagores theorem ,…

Q: On your written working, show that for any angles A and B, the following identity holds sin A cos B…

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Q: For angles u and v in quadrant II, if  sin u =3/5 and cos v= -  5/13 ,  find the exact value of…

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