Given that sin x + sin y = a and cos x + cos y =a, where a not equal to 0, express sin x + cos x in terms of a.
attemp:
sin x = a  sin y
cos x = a  cos y
sin x + cos x = 2A  (sin y + cos y)
 👍
 👎
 👁
 ℹ️
 🚩
2 answers

so sinx + siny = cosx + cosy
the trivial and obvious solution is x = y = 45° or π/4
another obvious one is 225° or 5π/4, because of the CAST rule
are there others , not multiples of 45°
recall:
sin a + sin b = 2 sin (1/2)(a+b) cos (1/2)(ab)
cos a + cos b = 2 cos (1/2)(a+b) cos (1/2)(ab)
so:
sinx + siny = 2 sin (1/2)(x+y) cos (1/2)(xy)
cosx + cosy = 2 cos (1/2)(x+y) cos (1/2)(xy)
2 sin (1/2)(x+y) cos (1/2)(xy) = 2 cos (1/2)(x+y) cos (1/2)(xy)
divide both sides by 2cos (1/2)(xy)
sin (1/2)(x+y) = cos (1/2)(x+y)
divide by cos (1/2)(x+y)
tan (1/2)(x+y) = 1
we know tan 45° = 1
(1/2)(x+y) = 45
x+y = 90
so any pair of complimentary angles will work
e.g let x = 10°, y = 80°
LS = sin10° + sin80°
= cos80° + sin10
= RS
of course, I should have seen the property that
cosØ = sin(90° Ø)
then sinx + siny = sin(90x) + sin(90y)
sinx + siny = sin90cosx  cos90sinx + sin90cosy  cos90siny
sinx + siny = (1)cosx  (0)sinx + (1)cosy  (0)siny
sinx + siny = cosx + cosx
back to the beginning 👍
 👎
 ℹ️
 🚩
answered by Reiny 
not answered.
Question asked: express sinx + cosx in term of a. 👍
 👎
 ℹ️
 🚩
answered by LC
Answer this Question
Related Questions

Calculus
Find d^5/dx^5 g(x) for g(x)=sinx+5x^4 A. cos x B. sin x + 120 C. cos x +20x^3 D. cos x + 120 x E. sin x
 asked by Stephanie

PreCalc
1) Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number. cos 12° cos 18° − sin 12° sin 18° And Find its exact value. 2) Use an Addition or Subtraction Formula to write the expression as a
 asked by Alyssa

Calculus
For the functions f(x) = sin x, show with the aid of the elementary formula sin^2 A = 1/2(1cos 2A) that f(x+y)  f(x) = cos x sin y2 sin x sin^2 (1/2y).
 asked by Anonymous

Trig
Find all solutions w between 0 and 360, inclusive: (a) cosw = cos(−340) (b) cosw = sin 20 (c) sinw = cos(−10) (d) sin w < − 1/2 (e) 1 < tanw
 asked by sally

Math, please help
Which of the following are trigonometric identities? (Can be more then one answer) tanx cosx cscx = 1 secxcosx/secs=sin^2x 1tanxtany=cos(x+y)/cosxcosy 4cosx sinx = 2cosx + 1  2sinx Find all solutions to the equation cosx cos(3x)  sinx sin(3x) = 0 on
 asked by Jill

trig  identies
Assume that A and B are in standard position and that sin A = 1/2, cos A >0, tan B = 3/4, and sinB
 asked by Anonymous

Calc 3
Calculate the velocity and acceleration vectors, and speed for r(t)=⟨cos(6t),sin(t),sin(6t)⟩ when t=5π/6 .
 asked by ally

calculus
Which of the following are antiderivatives of f(x)=sinxcosx? I f(x)=(sin^2* x)/2 II f(x)=(cos^2* x)/2 III f(x)=cos(2x)/4
 asked by Tiffany

calculus
Find the points on the curve y= (cos x)/(2 + sin x) at which the tangent is horizontal. I am not sure, but would I find the derivative first: y'= [(2 + sin x)(sin x)  (cos x)(cos x)]/(2 + sin x)^2 But then I don't know what to do or if that is even
 asked by CMM

Math
Suppose f(x) = sin(pi*cosx) On any interval where the inverse function y = f –1(x) exists, the derivative of f –1(x) with respect to x is: a)1/(cos(pi*cosx)), where x and y are related by the equation (satisfy the equation) x=sin(pi*cosy)
 asked by Thomas

Math
If sin(x) = 4/5 and cos(y) = 5/13 with both x and y terminating in quadrant 1 find the exact value of cos(xy) I know that the denominator will be 65
 asked by Bryan

college Physics
The coordinates of an object moving in the xy plane vary with time according to the following equations x = −7.16 sin ùt and y = 4.00 − 7.16 cos ùt, where ù is a constant, x and y are in meters, and t is in seconds. Write expressions for the
 asked by Katie

selfstudy calculus
Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t increases. r(t)=cos(t)I cos(t)j+sin(t)k I don't know what to do. I let x=cos(t), y=cos(t) and z= sin(t). Should I let t be any number and get the equal
 asked by Anonymous

math
Find the values of sin θ, cos θ, and tan θ for the given right triangle (in the link below). Give the exact values. www.webassign.net/aufexc2/85003.gif sin θ= cos θ= tan θ= my answer is c^2 = a^2 +b^2 c^2 = 5^2+12^2 c^2 = 169 c= √(169) c= 13 I
 asked by anonymous

Math
A right triangle has acute angles C and D. If tan C=158 and cos D=1517, what are cot D and sin C? cot D=8/15 and sin C=8/17 cot D=8/15 and sin C=15/17 cot D=15/8 and sin C=15/17 cot D=15/8 and sin C=8/17
 asked by m

math
Can you please check my work. A particle is moving with the given data. Find the position of the particle. a(t) = cos(t) + sin(t) s(0) = 2 v(0) = 6 a(t) = cos(t) + sin(t) v(t) = sin(t)  cos(t) + C s(t) = cos(t)  sin(t) + Cx + D 6 = v(0) = sin(0) cos(0)
 asked by Kay

Calculus 3
Let r(t) = < sin(6t), cos(6t), sin(6t)cos(12t) >. Find the point where r(t) intersects the xyplane on the interval π/6 < t < 3/12π.
 asked by EKM

Math
Jasmine is flying a kite. She lets out 86 feet of string. She takes the kite into the ground and measures the angle. The string forms a 47° angle with the ground. Which expression could be used to determine how high above the ground the kite is flying? A)
 asked by Help me pls FAST

calculus
Find complete length of curve r=a sin^3(theta/3). I have gone thus (theta written as t) r^2= a^2 sin^6 t/3 and (dr/dt)^2=a^2 sin^4(t/3)cos^2(t/3) s=Int Sqrt[a^2 sin^6 t/3+a^2 sin^4(t/3)cos^2(t/3)]dt =a Int Sqrt[sin^4(t/3){(sin^2(t/3)+cos^2(t/3)}]dt=a Int
 asked by ms

Trig
A. Find simpler, equivalent expressions for the following. Justify your answers. (a) sin(180 + è) (b) cos(180 + è) (c) tan(180 + è) B. Show that there are at least two ways to calculate the angle formed by the vectors [cos 19, sin 19] and [cos 54, sin
 asked by sally
Still need help?
You can ask a new question or browse existing questions.