Question
If x = p sin theater and y = p cos theater show that x square + y square = p square .
Answers
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To prove that x^2 + y^2 = p^2, we simply need to substitute the given values of x and y in terms of p and theta into the equation and simplify:
x^2 + y^2 = (p sin(theta))^2 + (p cos(theta))^2
= p^2(sin^2(theta) + cos^2(theta))
= p^2(1) (since sin^2(theta) + cos^2(theta) = 1)
= p^2
Therefore, we have shown that x^2 + y^2 = p^2, which is the desired result.
x^2 + y^2 = (p sin(theta))^2 + (p cos(theta))^2
= p^2(sin^2(theta) + cos^2(theta))
= p^2(1) (since sin^2(theta) + cos^2(theta) = 1)
= p^2
Therefore, we have shown that x^2 + y^2 = p^2, which is the desired result.