It has been observed since ancient times that light refracts or "bends" as it travels from one medium to another (from air to water, for example). If v, is the speed of light in one medium and vz its speed in another medium, then according to Snell's Law, sin(e,) sin(82) where 8, is the angle of incidence and 8, is the angle of refraction (see the figure). The number v/v, is called the index of refraction. The index of refraction for several substances is given in the table. Refraction Air from air Substance to substance Water 1.33 Alcohol 1.36 Water Glass 1.52 Diamond 2.41 If a ray of light passes through the surface of a lake at an angle of incidence of 75°, what is the angle of refraction? (Round your answer to two decimal places.)

Q: 6. B In right triangle ABC above, what is sin B?

A: Given, The right triangle ABC with right angle at C Where AB=8, BC =5  and  CA = 6 We have to find…

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Q: Find sin (- if tan u = 15.533 and u is in Quadrant-IV. sin) = Your answer should be accurate to 4…

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Q: If sec ? = 16 , find sin ?. (This should be an exact answer, not a decimal approximation.)

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Q: .If Sin 0 = 3/ 5 , find without using tables the values of : i) Cos 0 i) tan 0 (ans: ) 4/5; ij 34)…

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Q: Find the exact value of the expressions cos(a + B), sin(a + B) and tan(a + B) under the following…

A: Use quadrant to solve

Q: Find sin(2x), cos(2x), and tan(2x) from the given information. sin(x) = 5/13, x in Quadrant I

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Q: Find the remaining trigonometric ratios of 0 based on the given information. V3 and 8 is not in QIII…

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Q: (유) 8 Find the EXACT value of sin(A + B) if angle A is arctan and angle B is arcsin 17 sin(A + B) -

A: Given ∠A=arctan43 and ∠B=arcsin817. We have to find the exact value of sinA+B. Use formula,…

Q: If sin e= and 0<es, find the exact value of tan 20. %3D 4 24 24 4

A: Given,        sinθ=35 and 0≤θ≤π2

Q: 13п What is the exact value of sin-(x) if x =cot 4 A 4 B 4 D 티2

A: Option (c) π2

Q: snip

A: To Show: a formula for the altitude h from a vertex to the opposite side a of a triangle…

Q: Give the EXACT values for the quantities. (a) sin 19 (b) cos (c) cos = COS

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Q: If {(2 sin e - cos 0) / (cos 0 + sin 0)} = 1, then the value of cot 0 is

A: Introduction :

Q: If a e" sec 0, y = e' tan 0, show that Hr,e) (r,0) 1 (1,y) E E E

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Q: From the formula of sin (A + B), deduce the formulae of cos(A+ B) and cos (A- B).

A: To derive formula cos(A+B) &amp; cos(A-B) using formula of sin(A+B)

Q: Find the exact value of sin(u-v) given that sin u = 15/17 and sin v =12/13, with u and v in quadrant…

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Q: If AC = 3 and BC = 2, find the following quantities. (E sin A, cos A, tan A sin A = cos A =

A: It is given that, ∆ABC is a right triangle with ∠C=90° If AC=3 and BC=2

Q: In a right triangle, one acute angle measures X°. If cos(x)= 3/4, what is the sin(90-x)?

A: In a right triangle,  Cos(x) = 3/4 We have to find sin(90-x)

Q: Evaluate the expression under the given conditions. 2/5 sin(e + g); sin(e) e in Quadrant I, cos(@)…

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Q: In a right triangle = x and cos B= y which expression represents the value of sin C + cos C O y+x O…

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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: Given sin ß = in QII, and is on the terminal side of a the exact value of: • sin(a + B)

A: Given: sinβ=513

Q: If sin z + cos I 2, then the value of sin" r+ cos" z will be-

A:

Q: A line makes the same angle e with each of the X- and Z- axis. If the angle B, which it makes with…

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Q: 19 21 Choose the function that could be used to find the measure of the angle with the "?". sin COS…

A: Given: A right-angled triangle with hypotenuse 21 units, and a side as 19 units. From the unknown…

Q: Find the exact value of the expressions cos(a B), sin(a B) and tan(a + B) under the following…

A: Given,

Q: E sin i sin 98 cos 50 de

A:

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: 2. If sin 0 = and e is in the second quadrant, find tan, 0.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find sin A, cos A, tan A, and sin B, cos B, and tan B in right triangle ABC, with C=90 degree b=1…

A:

Q: Suppose cos(α)=−3/4 and sin(α) is negative. If the point (−3,y) is on the terminal side of the…

A: Use trigonometric ratio  &amp; its identity

Q: Find sin u and cos u if the given point lies on the terminal side of u.     (3,-4)

A: R=x2+y2sin u= y/Rcos u=x/R

Q: (금) 7 Suppose that is an angle in quadrant 3 and that cos y = Compute the exact value of sin 25 sin…

A: Given, cosγ = -725  γ2 is an angle in quadrant 3  We have to find the exact value of sinγ2.

Q: Given that sin' (x) and cos ( x), show that sin(a+B) = 1

A: Given that sin^-1 (x) and cos^-1(x) We have to prove that sin ( alpha + beta) = 1

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

A: The solution is :

Q: If sin A = 15/17, sin B = 5/13, cosA = 8/17, andcosB = 12/13, what is the exact value of sin(A – B)…

A: Here we find the value of Sin(A-B)

Q: 5 and cos a= 13 If sin a 12 , what is the value of sec a + )? 13 O 17/2 26 O 7/2 26 O 13/2 17 O 13…

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Q: Given: tan θ=12/5 What is the trigonometric ratio of cos θ?

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Q: 1. 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: Draw the diagram according to the question.

Q: If sin a cos 31° + cos z sin 31° =0.7, then the value of x, where 0° <x <90°, to the nearest whole…

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Q: 4. Apply half-angle formula to find b. sin 15° 5m C. COS a. cos 15°

A: The half-angle formulas are: sinθ2=±1-cosθ2cosθ2=±1+cosθ2   We know that the sine function is…

Q: The formula for cos(at B) is cos a cos B - sin a sin B cos a cos B + sin asin B sin a sin B - cos a…

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Q: GIven that cose= 3 Sin e0 %3D find Sin 20 Cos 20 tan 20

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Q: It is known that sin A =, where < A < n, and cos B = n< B < . Find the exact values of: where 13 3x…

A: Given that, sinA=35,π2&lt;A&lt;πcosA=-513,π&lt;B&lt;3π2

Q: By comparing e3i0 = cos 30 + i sin 30 with ( ei8)3 = ( cos 0 + i sin 0)3, find the "triple angle"…

A: Euler's rule: ei3θ = cos3θ + i sin3θ   -------------------Eqn (1) Also, (eiθ)3 = (cosθ + i sinθ)3

Q: In right triangle ABC, m/B mZC. Let sin B = r and cos B = s. C Which expression represents the value…

A: