HPC 1.1-1.3 practice 2

Find [math]\sin {\theta}[/math] and [math]\cos {\theta}[/math] if [math]cot{\theta}=\dfrac{8}{15}[/math] and [math]\sec {\theta}<0[/math]

If [math]\sin x = m[/math] and [math]0^{\circ}<\theta<90^{\circ}[/math], then [math]\tan x =[/math]

Find the [math]x[/math]-coordinate such that point [math](x,y)[/math] on the unit circle that corresponds to the real number [math]\theta=-\dfrac{2\pi}{3}[/math]

Find the value of [math]8\sin\left(\dfrac{\pi}{3}\right)\cos\left(-\dfrac{7\pi}{6}\right)[/math].

Consider the following numbers:
[math]a=\sec\left(\dfrac{5\pi}{3}\right)[/math]
[math]b=\tan\left(\dfrac{5\pi}{3}\right)[/math]
[math]c=\csc\left(\dfrac{-\pi}{2}\right)[/math]
[math]d=\sin\left(\dfrac{13\pi}{6}\right)[/math]
[math]e=\cot\left(\dfrac{13\pi}{6}\right)[/math]
[math]f=\cos\left(\dfrac{-\pi}{4}-2000\pi\right)[/math]
How many numbers are negative and irrational?

Which of the following angles is not co-terminal to the others?

Given the graph below, determine the equation of the graph.

The Ferris wheel shown in this figure makes one complete turn every 20 seconds. A rider’s height, h, above the ground can be modeled by the equation [math]h=a \sin \omega t+k[/math], where [math]h[/math] and [math]k[/math] are given in feet and [math]t[/math] is given in seconds.

(a) What is the value of [math]a[/math]?

(b) What is the value of [math]k[/math]?

(c) What is the value of [math]\omega[/math]?

An object in simple harmonic motion has a frequency of [math]\dfrac{1}{4}[/math] oscillation per minute and an amplitude of 8 feet. Write an equation in the form [math]d= \alpha \sin( \omega t )[/math] for the object’s simple harmonic motion.

What is the period of the function [math]f(x)=100\cos(200x-300)+400[/math]?