Final answer:
The student inquired about solutions to 'sin z = 100', which has no real solutions, but could be addressed using complex analysis. Another part of the question involves reducing light intensity by 90%, using the equation 'I = Io cos² θ' to determine the necessary angle of light. Additional details were provided, but some mathematical formulas in the original question were incorrect or incomplete.
Step-by-step explanation:
The student is asking for solutions of the equation sin z = 100. In the context of traditional real number trigonometry, this question doesn't have solutions because the sine function for real numbers only takes on values from -1 to 1. However, if we consider the complex plane, the sine function can take on any complex number value. Even with this consideration, solving such an equation is beyond the scope of typical high school mathematics, and typically one would use complex analysis to solve it.
To solve the equation I = Io cos² θ when the intensity I has been reduced by 90%, we understand that I is 10% of Io, which can be written as I = 0.100 * Io. Then substitute 0.100 * Io for I and solve for cos theta (cos θ), and eventually for θ itself, using inverse trigonometric functions. This process finds the angle θ needed when a light's intensity is reduced. For the simple harmonic oscillator, the equation to find the magnitude of the velocity as a function of position is given incorrectly above; the correct form should involve kinetic and potential energy considerations, which are not shown in the provided text.