For any triangle, derive the formula a = b cos C + c cos B [Hint: Use the fact that sin A = sin(180° - B - C).]

Q: O a) -a Ob) -b Oc) b O d) a

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Q: Consider a right triangle with two other angles A and B.  Find the value of sin (A) if cos (A)=3/5?

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

Q: For positive acute angles A and B, it is known that cos A= 9/41 and tan B=21/20. Find the value of…

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Q: For any angle o in standard position, let P = (x, y) be the point on the terminal side of 0 that is…

A: For any angle θ in standard position P(x,y) be the point on the terminal side of θ that is also on…

Q: When using the half-angle formula for sin (A/2) or cos (A/2), the sign in front of theradical is…

A: When using the half-angle formula for sin (A/2) or cos (A/2), the sign in front of theradical is…

Q: For the right triangle shown, express the sin of θ in terms of sides a, b, and c.

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Q: A student uses a protractor to measure an angle to be 0 = 85° ± 1°. What should she report for sin 0…

A: We know that, the uncertainty in sin(θ) can be found either from half the difference between the…

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

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

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Q: If sin 12 1 A – VB, then, by using a half-angle formula, find 2 A В -

A: We know that the half range formula is sinθ2=1-cosθ2. Here, θ=π6.

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

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Q: Drag the label for the length of the sides of the triangle shown that would satisfy the following…

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Q: In the given figure, AABC is a right triangle. What is true about AABC? OA. sin(A) = sin(C) and…

A: We know that in triangle sum of all 3 angles is 180°A+B+C=180B=90°A+90+C=180A+C=180-90A+C=90A=90-C…

Q: The sine of any acute angle must be greater than____-and less than____?

A: Let the acute angle is θ We have the interval of acute angle 0<θ<π2

Q: For any angle 0 in standard position, let P = (x, y) be the point on the terminal side of 0 that is…

A: Given : For any angle θ in standard position, let P = ( x, y) be the point on the terminal side of θ…

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

A: Given,          cosu=-1517 ,  π2<u<π

Q: To answer the following. Explain why there is no angle theta such that sec theta = 1/2.

A: Given that secθ=12

Q: If sin =VA – VB, then, by using a half-angle formula, find

A: Here, the given expression is: sinπ12=12A-B

Q: For the right triangle shown, express each of the following in terms of a, b, and c: a) sin a b) tan…

A: here we have to find , .a) sinα b) tanβ

Q: when the axes are related through an angle a ,find the trafsformed equation of x cos a +y sina =p

A: The given equation is: x cos a+y sin a=p to rotate the equation through an angle a.

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: find the angle θ between v and w. If necessary, round to the nearest tenth of a degree. v = cos…

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Q: "For the right triangle shown, express the cos of ∅ as a fraction in lowest terms if side a=8, side…

A: The edge length of the right-angled triangle  is  a=8, side b=6 and side c = 10 We need to find as…

Q: For an acute angle 0, the equation sin(8)=cos(6) is true. What is the value of 0?

A: solution  given below..

Q: Consider right triangle ADEF below. E F D Which expressions are equivalent to cos(ZE)?

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Q: For the right triangle shown, express the sin of ∅ in terms of a,b, and c.

A: Given: The right angle triangle shown in the figure, We have to find sin∅

Q: CoS * and sin o-

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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: Identify the cos >0, sec 0 >0 quadrant(s) of an angle that satisfies the given conditions.

A: Given cos θ>0,  sec θ>0     The figure (CAST diagram) below indicates the quadrants…

Q: If sin(A+ 60°) = cos 2A where 2A is an acute angle, then find the value of A

A: We have to find the value of A where 2A is an acute angle and given that: sin A+60°=cos 2A We know…

Q: Find the angle 0 between and 37 such that sec(0) = – /2. -

A: We can solve the problem by finding the angle between the interval.

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: Prove the Law of Cosines, c² = a² + b² – 2ab cos 0, by referring to Figure 23. Hint: Consider the…

A: To prove :                   The Law of Cosines. From the given figure, it is observed that x = a…

Q: COS Cos e and tan tan D = 2/2 %3D

A: A unit circle used to verify trigonometric ratios is constructed as follows:- The ratios from the…

Q: Assuming all angles are acute, what is the solution for the following equation: sin A = cos 8A

A: The given equation is  sin A = cos 8A

Q: Consider the angle θ in standard position with the terminal side passing through P(4.4,4.3).  Find…

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Q: If sin 15° = vA – VB, then, by using a half-angle formula, find

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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, 0 < 0 < 2r, to find the exact value of: tan 0 = } ; n< 0<…

A: Given: tanθ=12; π&lt;θ&lt;3π2

Q: In triangle ABC, 2C is a right angle. If cos(A) = and sin(A) = † , what is tan(A) ? %3D A) B)

A: tan(A)= sin(A)/cos(A)

Q: For the right triangle shown express the cos of θ as a fraction in lowest terms. Side a = 6, side b…

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Q: If θ is an acute angle and cos θ = 1/3, find csc (π/2 - θ).

A: It is given that,cos θ = 1/3 We have to find  csc (π/2 - θ).

Q: If the angle 0 is in standard position and P(x, y) is a point on the terminal side of 0, and r is…

A: The figure is and solution is shown in step. 2

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: For an acute angle 0, given the equation sin(0) = cos( 38 ) What is the value of 0?

A: sin(90-θ) = cosθ