Question

Assume sin t = 0.45 and sin w = 0.89, both t and w are positive values between 0 and 2π , and both t and w determine a terminal point in quadrant 1. Which statements best describes the relationship between t and w?

A: w > t
B: t > w
C: It is not possible to tell from the given information.

If sinθ = 4/5 and θ is in quadrant 2, the value of cot θ is ____. If necessary, use the slash mark (/) for a fraction bar.

Answer 1

Answer on Question #57983 – Math – Trigonometry

Question

Assume $\sin t = 0.45$ and $\sin w = 0.89$, both $t$ and $w$ are positive values between 0 and $2\pi$, and both $t$ and $w$ determine a terminal point in quadrant 1. Which statements best describes the relationship between $t$ and $w$?

A: $w > t$

B: $t > w$

C: It is not possible to tell from the given information.

Solution

Given both $t$ and $w$ determine a terminal point in quadrant 1, if $\sin w > \sin t$ then $w > t$.

Answer: A. $w > t$.

Question

If $\sin\theta = 4/5$ and $\theta$ is in quadrant 2, the value of $\cot\theta$ is ___. If necessary, use the slash mark (/) for a fraction bar.

Solution

If $\theta$ belongs to quadrant 2 then $\cos\theta < 0$. By the Pythagorean identity, $\cos^2\theta + \sin^2\theta = 1$. It follows from both previous statements that $\cos\theta = -\sqrt{1 - \sin^2\theta}$.

Next,

$\cot\theta = \cos\theta / \sin\theta = -\sqrt{1 - \sin^2\theta} / \sin\theta = -\sqrt{1 - 0.64} / 0.8 = -0.6 / 0.8 = -0.75.$

Answer: -0.75.

www.AssignmentExpert.com