हिंदी

Find the Cartesian coordinates of the point whose polar coordinates are : (4, π2) - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Find the Cartesian coordinates of the point whose polar coordinates are :

`(4,  pi/2)`

योग

उत्तर

Here,

r = 4 and θ = `pi/2`

Let the cartesian coordinates be (x, y)
Then, x = rcos θ = 4cos `(π/2)` = 0
y = r sin θ = 4sin`(π/2)`= 4
∴ The cartesian coordinates of the given point are (0, 4).

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Trigonometric Functions - Exercise 3.2 [पृष्ठ ८८]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Arts and Science) [English] 12 Standard HSC Maharashtra State Board
अध्याय 3 Trigonometric Functions
Exercise 3.2 | Q 1.2 | पृष्ठ ८८

संबंधित प्रश्न

In a Δ ABC, with usual notations prove that:` (a -bcos C) /(b -a cos C )= cos B/ cos A`


In ΔABC, prove that `tan((A - B)/2) = (a - b)/(a + b)*cot  C/2`


 

In ΔABC with usual notations, prove that 2a `{sin^2(C/2)+csin^2 (A/2)}` = (a +   c - b)

 

In any ΔABC, with usual notations, prove that b2 = c2 + a2 – 2ca cos B.


The angles of the ΔABC are in A.P. and b:c=`sqrt3:sqrt2` then find`angleA,angleB,angleC`

 


With usual notations, in ΔABC, prove that a(b cos C − c cos B) = b2 − c2


Find the Cartesian co-ordinates of the point whose polar co-ordinates are:

`(sqrt(2), pi/4)`


Find the Cartesian co-ordinates of the point whose polar co-ordinates are:

`(1/2, (7pi)/3)`


Find the polar co-ordinates of the point whose Cartesian co-ordinates are.

`(1, - sqrt(3))`


Solve the triangle in which a = `(sqrt3 + 1)`, b = `(sqrt3 - 1)` and ∠C = 60°.


In any Δ ABC, prove the following:

a sin A - b sin B = c sin (A - B)


In any ΔABC, prove the following:

`("c" - "b cos A")/("b" - "c cos A") = ("cos B")/("cos C")`


In any Δ ABC, prove the following:

a2 sin (B - C) = (b2 - c2) sin A.


In any Δ ABC, prove the following:

`"cos 2A"/"a"^2 - "cos 2B"/"b"^2 = 1/"a"^2 - 1/"b"^2`


In Δ ABC, if sin2 A + sin2 B = sin2 C, then show that the triangle is a right-angled triangle.


In Δ ABC, prove that a2 (cos2 B - cos2 C) + b2 (cos2 C - cos2 A) + c2 (cos2 A - cos2 B) = 0.


Show that `2 sin^-1 (3/5) = tan^-1(24/7)`


Show that

`tan^-1(1/5) + tan^-1(1/7) + tan^-1(1/3) + tan^-1 (1/8) = pi/4.`


Prove that `tan^-1 sqrt"x" = 1/2 cos^-1 ((1 - "x")/(1 + "x"))`, if x ∈ [0, 1]


Show that `(9pi)/8 - 9/4 sin^-1 (1/3) = 9/4 sin^-1 ((2sqrt2)/3)`.


If `tan^-1 (("x" - 1)/("x" - 2)) + tan^-1 (("x" + 1)/("x" + 2)) = pi/4`, find the value of x.


In ∆ABC, if cos A = `(sinB)/(2sinC)`, then ∆ABC is ______.


In ∆ABC, if ∠A = 30°, ∠B = 60°, then the ratio of sides is ______.


If polar co-ordinates of a point are `(3/4, (3pi)/4)`, then its Cartesian co-ordinate are ______


In ∆ABC, prove that ac cos B − bc cos A = a2 − b2 


In ∆ABC, if sin2A + sin2B = sin2C, then show that a2 + b2 = c2 


Find the polar co-ordinates of point whose Cartesian co-ordinates are `(1, sqrt(3))`


Find the Cartesian co-ordinates of point whose polar co-ordinates are `(4, pi/3)`


In ∆ABC, if a = 13, b = 14, c = 15, then find the value of cos B


In ∆ABC, prove that `(cos 2"A")/"a"^2 - (cos 2"c")/"c"^2 = 1/"a"^2 - 1/"c"^2`


In ∆ABC, prove that `sin  ((A - B)/2) = ((a - b)/c) cos  C/2` 


If the angles A, B, C of ΔABC are in A.P. and its sides a, b, c are in G.P., then show that a2, b2, c2 are in A.P.


In ∆ABC, prove that `(cos^2"A" - cos^2"B")/("a" + "b") + (cos^2"B" - cos^2"C")/("b" + "c") + (cos^2"C" - cos^2"A")/("c" + "a")` = 0


In ΔABC, a(cos2B + cos2C) + cos A(c cos C + b cos B) = ?


In a triangle ABC with usual notations, if `(cos "A")/"a" = (cos "B")/"b" = (cos "C")/"c"`, then area of triangle ABC with a = `sqrt6` is ____________.


In Δ ABC; with usual notations, if cos A = `(sin "B")/(sin "C")`, then the triangle is _______.


In a ΔABC, `(sin  "C"/2)/(cos(("A" - "B")/2))` = ______ 


In a ΔABC, 2ab sin`((A + B - C)/2)` = ______


If P(6, 10, 10), Q(1, 0, -5), R(6, -10, λ) are vertices of a triangle right angled at Q, then value of λ is ______.


In Δ ABC; with usual notations, `("b" sin "B" - "c" sin "C")/(sin ("B - C"))` = _______.


The polar co-ordinates of P are `(2, pi/6)`. If Q is the image of P about the X-axis then the polar co-ordinates of Q are ______.


In ΔABC, `(sin(B - C))/(sin(B + C))` = ______


In Δ ABC, with the usual notations, if `(tan  "A"/2)(tan  "B"/2) = 3/4` then a + b = ______.


In ΔABC if sin2A + sin2B = sin2C and l(AB) = 10, then the maximum value of the area of ΔABC is ______ 


In ΔABC, if `cosA/a = cosB/b,` then triangle ABC is ______ 


If cartesian co-ordinates of a point are `(1, -sqrt3)`, then its polar co-ordinates are ______ 


In ΔABC, a = 7cm, b = 3cm and c = 8 cm, then angle A is ______ 


In any triangle ABC, the simplified form of `(cos2A)/a^2 - (cos2B)/b^2` is ______


If polar co-ordinates of a point are `(1/2, pi/2)`, then its cartesian co-ordinates are ______.


If in Δ ABC, 3a = b + c, then `cot ("B"/2) cot ("C"/2)` = ______.


If PQ and PR are the two sides of a triangle, then the angle between them which gives maximum area of the triangle is ______.


In `triangleABC,` if a = 3, b = 4, c = 5, then sin 2B = ______.


If in ΔABC, `sin  "B"/2 sin  "C"/2 = sin  "A"/2` and 2s is the perimeter of the triangle, then s is ______.


If a = 13, b = 14, c = 15, then `cos("A"/2)` = ______.


In a ΔABC, if `("b" + "c")/11 = ("c" + "a")/12 = ("a" + "b")/13`, then cos C = ______.


In triangle ABC, a = 4, b = 3 and ∠A = 60°. If ' c' is a root of the equation c2 – 3c – k = 0. Then k = ______. (with usual notations)


The number of solutions of the equation sin 2x – 2 cosx + 4 sinx = 4 in the interval [0, 5π] is ______.


Let ABC be a triangle such that ∠A = 45°, ∠B = 75° then `"a" + "c"sqrt(2)` is equal to ______. (in usual notation)


If in a ΔABC `a cos^2(C/2) + c cos^2(A/2) = (3b)/2`, then the sides a, b and c ______.


In a triangle ABC, ∠C = 90°, then `(a^2 - b^2)/(a^2 + b^2)` is ______.


In ΔABC, with usual notations, if a, b, c are in A.P. Then `a cos^2 (C/2) + c cos^2(A/2)` = ______.


If in ΔABC, `sin  A/2 * sin  C/2 = sin  B/2` and 2s is the perimeter of the triangle, then s = ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×