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Standard X

Mathematics

Range of Trigonometric Ratios from 0 to 90 Degrees

If x=r sinθco...

Question

If x = r sin θ cos ϕ, y = r sin θ sin ϕ and z = r cos θ, then

(a) $x^{2} + y^{2} + z^{2} = r^{2}$
(b) $x^{2} + y^{2} - z^{2} = r^{2}$
(c) $x^{2} - y^{2} + z^{2} = r^{2}$
(d) $z^{2} + y^{2} - x^{2} = r^{2}$

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Solution

Given:

Squaring and adding these equations, we get

Hence, the correct option is (a).

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If x = r sin θ cos ϕ, y = r sin θ sin ϕ and z = r cos θ, then (a) x2+y2+z2=r2 (b) x2+y2-z2=r2 (c) x2-y2+z2=r2 (d) z2+y2-x2=r2

Given: Squaring and adding these equations, we get Hence, the correct option is (a).

If x = r sin θ cos ϕ, y = r sin θ sin ϕ and z = r cos θ, then

(a) $x^{2} + y^{2} + z^{2} = r^{2}$
(b) $x^{2} + y^{2} - z^{2} = r^{2}$
(c) $x^{2} - y^{2} + z^{2} = r^{2}$
(d) $z^{2} + y^{2} - x^{2} = r^{2}$

Given:

Squaring and adding these equations, we get

Hence, the correct option is (a).