Q3: Find Fourier frans for m for below sign a ls? O fit)= 3 rect (t) ,O fit)= 8rut(t ) 16 jat ® fit)= 6 sin'(10TC+) .Ofit = 6 cos(I9Tet - I 3

Q: cos\theta =(1)/(3)and \theta  is in quadrant IV, then cos(\theta )/(2)

A:

Q: verify that cos(alpha-beta)/sin of alpha sin of beta is = cot of alpha cot of beta +1  please show…

A:

Q: 1.) xyax ^)/√²-1²) dx + (x² - 2xy) dy = 0

A: Given : x2-y2dx+x2-2xydy=0 To Check : Differential equation is exact or not

Q: 2 arcsin ++2rk, ±- 4 - 2rk + 2жk 4 ±"+27k, ±- 4 - 27rk + 2жk 4 57 + + 2rk, ±- 4 - 2rk 4 ++2rk, ±: 4…

A: sin-(-2/2) 2/2 = 1/2 sin-(-1/2) sin is negative in 3rd and 4th quadrant so here π + π/4 = 5π/4 and π…

Q: 4. Use an appropriate half angle identity to find the exact value of cos15°.

A:

Q: 2. Explain why arcsin(sin(0)) = 0 but arcsin(sin(807)) # 807

A: Concept  arcsin(sin x) = x   is true  only when x lie in the interval [-π/2 , π/2]

Q: (cscD+cotD)/(tanD+sinD)=cotDcscD

A:

Q: Find the arclength of fox) = Ln/sinx/ on [1, 2] Round the answer to 2 decimals.

A:

Q: sin [cot(4e¬4*)]cos*[cot(4e¬4*)] dx e^x sin²(4e¬4x) Let u = cot(4e¬4x) %3D

A: Solution: Let the given integral is I=∫sin6cot4e-4xcos4cot4e-4xdxe4xsin24e-4x ......(1) Substitute…

Q: Find Modulus and arg for: fal tand - (b) 1-Cosx +isind 1+ Sind-i Cosa

A:

Q: ZA'B'C' is the image of LABC following the reflec- tion of ZABC across line (. If mZA'B'C'= + 20 and…

A: Given: m∠A'B'C'=x5+20, m∠ABC=x2+5 We know that when we take reflection of a triangle across any line…

Q: 5. Sketch the graph of r=2 cos 30 over over [0, a] (use x on [-3, 3] and y on [-3, 3] when using…

A: Solution: Given: r=2cos3θ ,[0,2pi] We are here using the graphing calculator to making graph.

Q: f (x) = 7X 0< RくL 1<スc2

A:

Q: Consider the function y=sin0, where 0=u+v. Suppose that u = v. Show how the Sum and Difference…

A: We will see the ans in next step

Q: 5. sin³0 cos-20d0

A:

Q: 4л coS 씀Cos 즙Cs -sin sin 15 15 15

A: We have to find the exact value cosπ15cos4π15-sinπ15sin4π15.

Q: i sin°Hcos* () .3x, sin°cos* dx 10. 3 10

A:

Q: Find cos(sin^−1(−1/2))

A: Trigonometric

Q: (i) Prove that sec 3x(sin 3x-2sin' 3x)= tan 3xcos 6x. (ii) Hence find, for 0s.xs, the values of x in…

A: Trigonometric equation

Q: 7. Prove: cos(0 + 2) 7) = sine.

A:

Q: (sece +tane)(1+sine)de =

A: Evaluate ∫π6π4secθ+tanθ1+sinθdθ

Q: Use de Moivre’s theorem with n = 4 to prove that cos(4θ) = 8 cos^4 (θ) − 8 cos^2 (θ) + 1

A:

Q: Find the points of intersection between r 2 = 2 cos20 and r =- %3D 1- cose

A: We have to find the intersection between r2=2cos2θ and r=21-cosθ.

Q: D FLx)= sSine? do 3.

A:

Q: (sinx/ 1-cosx)=cscx + cotx   verify the identity

A:

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.