Determine whether the graph of the given equation will be a line, circle, rose curve, lemnis-cate, cardioid, or limaçon      r = 3 +5 sin theta

Q: Use the exact values from show thatthe following are true.   cos 2 theta 30 0   + sin 2 30 0 =1 cos ...

A: The values you will use : cos30∘=32sin30∘=12cos45∘=12sin45∘=12  

Q: Give the reciprocal of each number.   y/r

A: Find the reciprocal of the number yr.

Q: Find the area of triangle ABC given the following information.     a =5.4 ft, b = 4.3 ft, and c = 3....

A: a =5.4 ft., b = 4.3 ft., and c = 3.2 ft.   Formula used: A=ss-as-bs-c where s=a+b+c2

Q: 17) If a = 4b3 and c = 5a?b*, show that c 80b10

A: Given:a=4b3,c=5a2b4

Q: Every real number is also a complex number.   True or False

A: We know that a complex number has two parts real and imaginary.  A complex number is written in form...

Q: Force If you have ever ridden on a chair lift at a ski area and had it stop, you knowthat the chair ...

A: Let the cable making an angle 71.8∘ has tension of T1 and another cable making an angle of 74.8∘ has...

Q: Pythagorean Theorem The roof of a house is to extend up 13.5 feet above the ceiling,which is 36 feet...

A: Let x be the length of one side of the roof. Since the roof forms an isosceles triangle, therefore t...

Q: Verify each identity.     cot x = cos 3 x + cos x / sin 3 x - sin x

A: cos3x+cosxsin3x-sinx=2cos3x+x2cos3x-x22cos3x+x2sin3x-x2    ∵cosx+cosy=2cosx+y2cosx-y2& sinx-siny...

Q: Convert each of the following to radians without using a calculator.       225  0

A: Consider the given term 225°

Q: Graphing cotangent function: y=2cot(1/4x)

A: Given y=2cot14x

Q: The notation a + bi is called ________ form for a complex number, and the notationr(cos u + i sin u)...

A:  

Q: Prove the identity: cos2 ?+ cos2?tan2?= 1

A: Givencos2θ +cos2θ tan2θ =1

Q: Find all six trigonometric functions for theta if the point (-6, 8) lies on the terminal sideof thet...

A: From the given data: The distance from the origin to the x-axis is -6. The distance from the origin ...

Q: Identify the period and the phase shift from the following trigonometric equation. y = -3 csc 4

A: The given equation is y=-3csc12x-π4-5. The standard equation of cosecant function is y=A cscBx-C+D. ...

Q: Prove that each of the following identities is true.   1/ 1+ cos x  + 1/ 1- cos x  = 2  cosec 2 x

A: Here given as 11+cos x+11-cos x=2cosec2x

Q: Prove each identity.   sin (A + B) + sin (A - B) = 2 sin A cos B

A: We have to prove: sinA+B+sinA-B=2sinAcosB We know the formulae for trigonometric if two angle are in...

Q: Write each expression as an equivalent algebraic expression involving only x. (Assume xis positive.)...

A: Given: sin2tan-1x for solving this we assume tan-1x=θ and use formula sin2x=2sinxcosx so, tanθ=x sin...

Q: Use the Cofunction Theorem to fill in the blanks so that each expression becomes a truestatement.   ...

A: tan8°=cot _

Q: find the remaining trigonometric functions of theta based on thegiven information.  cos theta = 24/2...

A: Given that: cosθ=2425

Q: Write each of the following in terms of sin theta and cos theta; then simplify if possible.   cot th...

A: Given: cotθ-cosecθ we know that cotθ=cosθsinθ, cosecθ=1sinθ now putting values of cotθ, cosecθ in gi...

Q: Find all solutions to each of the following triangles:       B = 62 degree 40 ' , b = 6.78 inches, c...

A:  B = 62 degree 40 ' , b = 6.78 inches, c = 3.48 inches

Q: Find the area of triangle ABC given the following information.    A = 56.2 degree , b = 2.65 cm, and...

A:

Q: Identify the horizontal translation for the graph of y =1 +4 cos ( 3x +pi/2)     -pi/6

A: The given function is y=1+4cos3x+π2

Q: Let x = 30 0 and y = 45 0 in each of the expressions that follow,and then simplify each expression a...

A: Given:  x = 30 0 and y = 45 0

Q: 18) Which expression is equivalent to (9x²y^)-? (1) 3xy3 (2) 3xy3 (3) (4)

A: Given expression is equivalent to 9x2y6-12 It can be simplified as follows. 9x2y6-12=19x2y612=13xy32...

Q: Graph one complete cycle of each of the following. In each case, label the axes accuratelyand identi...

A: The given function is y=cosx-π2.

Q: Prove the identity whether it is true or false

A:

Q: Table 3 shows the average monthly attendance at LakeNacimiento in California. Find the equation of a...

A: Below graph and table shows the average monthly attendance at Lake Nacimiento in California.

Q: A store has issued two different coupons for its customers to use. One coupon gives customers $25 of...

A: A store has issued two different coupons for its customers to use. One coupon gives customers $25 of...

Q: Windshield Wiper An automobile windshield wiper 10 inches long rotates through anangle of 60 degree....

A: θ=60°, r1=10 inches and l=9 inches   Formula used: A=12r2θ

Q: Graphing cotangent functions: y=2cot(1/2x)

A: y=2cot12x The period of given function is π12=2π. There is no maximum or minimum value. Now, cot12x=...

Q: Sketch the graph of y =-1/2sin (px). Which of the following matches your graph?

A: Given curve: y=-12sinpx

Q: a)Prove that 2cotθ sin2 θ = sin2θ. b)Hence, solve the equation 4 cotθsin2θ =  √3 for 0 ≤ θ ≤360°.

A:

Q: 3) Use the given information to find (a) sin(s+t), and (b) tan(s+t) and (c) the quadrant of s+t. (a)...

A: Given: (a) cos s= 3/4 and sin t= 5/13, s and t are quadrant 1. (b) sin s=3/5 and sin t= -12/13, s in...

Q: Find the linear velocity of a point moving with uniform circular motion, if the point coversa distan...

A: From the data: s=6cm t=2 sec  

Q: True or false: If cos A is negative, then cos (A/2) is negative as well.

A:

Q: Suppose f(x)=(x−3)2f(x)=(x-3)2 and g(x)=√x+7g(x)=x+7. Evaluate the following expressions. f(g(7))=...

A:

Q: A hot-air balloon is flying over a dry lake when the wind stopsblowing. The balloon comes to a stop ...

A: In △ACD, tan 12∘=DCACAC=450tan 12∘=4500.2125≈2117 ft

Q: Solve the following equations on the interval [0,2pi), write a general solution.

A: