Question

If sec(x) = -root2 and pi/2

Answer 1

Answer: x = π - π/4 = 3π/4

Step-by-step explanation:

If sec(x) = -√2 and x is in the second quadrant (between π/2 and π), we can use the identity:

sec^2(x) - 1 = tan^2(x)

to find the value of tan(x):

sec^2(x) - 1 = tan^2(x)

(-√2)^2 - 1 = tan^2(x)

2 - 1 = tan^2(x)

1 = tan^2(x)

Taking the square root of both sides, we get:

tan(x) = ±1

Since x is in the second quadrant, the angle that satisfies tan(x) = 1 is π/4. Therefore, we have:

x = π - π/4 = 3π/4

Note that the angle that satisfies tan(x) = -1 is in the fourth quadrant, so it is not relevant to this problem.

Answer 2

The question seems to involve solving trigonometric and physics-related equations, specifically focusing on secant functions in trigonometry, simple harmonic motion estimations, and conservation of momentum in mechanics.

Step-by-step explanation:

It appears that the original question is incomplete, but based on the given snippets, the subject seems to revolve around various mathematical concepts including trigonometry and equations of motion. Without the full context, we can surmise that the student may be asking about solving trigonometric equations, utilizing secant (sec) functions, analyzing simple harmonic motion (SHM), and applying the principles of conservation of momentum, which are relevant to physics—specifically, mechanics.

In one of the excerpts, sec(x) is mentioned, which is the reciprocal of cosine. For example, if sec(x) = -√2, it implies that cos(x) = -1/√2. In the context of angles where pi/2 < x < pi (which defines angles in the second quadrant), x would correspond to an angle whose cosine yields a negative result, consistent with the properties of trigonometric functions in the second quadrant.

The other fragments suggest the application of equations related to physics, such as the derivation of an equation for the period of a torsional pendulum that involves simple harmonic motion, as well as the conservation of momentum in collisions, which is critical in finding velocities post-collision in a two-body system.