Snell's Law is an equation from optics which describes how a light ray behaves when it passes from one medium to another with different indices of refraction. It says that n1sin(⊖1) = n2sin(⊖2) where n1 and n2 are the indices of reffraction and ⊖1 and ⊖2 are the angles of incidence. Suppose that you measure n1=1.4, n2=0.9, and ⊖1=pi/6 a) simplify the equation using the values provided and convert it to a root-finding problem for ⊖2. (A root-finding problem is a problem in which f(x)=0 and the goal is to find x)   B) Use the Intermediate Value Theorem to show that a solution exists for ⊖2 between 0 and pi/2. Clearly show that the conditions of the theorem are met, and state the appropriate conclusion.

Q: If sin(A) = -and A is in Quadrant 3. (): Determine sec

A:

Q: Verify the identity. 4 sec? y - 4 cot( - y) =- 4 sec? y - 4 cot (- y) - 4 (sec² y - = 4

A:

Q: Assume z =x+ iy = re® , i = /-1

A: Topic:- algebra

Q: (4x?+q]!O "Cx)=

A:

Q: 3) Find y" if y= 9 sin x.

A:

Q: 16. Verify sin(180° – ) = sin e (SHOW WORK)

A: We know that sin(a-b)=sina cosb-cosa sinb

Q: Find the exact value of sin sin 3. 元一3 |3|

A:

Q: 꺼니 Sin (t) dt Cos? CE)

A:

Q: If cos theta = a then sin theta = 1/a

A: Given information: If cosθ=a then sinθ=1a

Q: In the accompanying diagram of right triangle ABC, AB = 3, BC= 4, AC= 5, and mZABC = 90. %3D Ap B >C…

A: By using trigonometry ratio formula, we calculate the required sine (C).

Q: How does sin 15 ° = ((√2-(√3))/2

A:

Q: 14) sin- 1 2 /-

A: 14. let x=sin-1(12)     x=π6                    (∵ sin(π6) = 12)

Q: Suppose the point (4,6) sits on a ray from the origin making an angle of A in standard position, and…

A: topic - trigonometric ratios

Q: cos C25+) Se sincas+) dt

A:

Q: Give the exact value of COS (-) + sin ( 3 V3 O1 2 2 O V2 O 1+v3

A: We need to find the exact value of the given trigonometric ratios.

Q: e" sin (5x) dr

A: I=∫exsin5x dx

Angles

In mathematics, angles constitute a very important part. Just like the concept of lines, an angle is a necessary figure that is used for measurement. How do you define its formation? It is formed when two or more lines meet at a point. The point at which two or more lines meet is known as the vertex. When the lines get inclined at this point, they do form various angles. Angles are measured from the vertex in terms of degrees.