Which of the following is equivalent to \(\csc A + \cot A \ \)?

The cartesian coordinates \((x,y)\) corresponding to the polar coordinates \((4,\frac{3π}{4})\) are,

For some angle \(\theta\), \(\sin \theta = 8/17\) and the terminal side is in the second quadrant. What is the value of \(\tan \theta + \cot \theta\)?

What is the amplitude and the period of the below trigonometric function?

If \(\tan ⁡α = y\) where \(α\) is an angle between \(\dfrac{5π}{4}\) and \(\dfrac{3π}{2}\), then what is \(\cos⁡ α + \sin⁡ α\) equal to?

For some angle \(x, \sin ⁡x = -\frac{\sqrt{3}}{2}\) and \(\sec x = 2\). Which option shows the size of angle \(x\)?

\(\tan \left(\dfrac{πx}{4}\right)\) is plotted on a graph paper for \(x∈ \left(-\dfrac{5}{3},\dfrac{5}{3}\right)\). Which option shows the correct graph for the function?

Two functions, \(f(\theta)\) and \(g(\theta)\), are defined as \(\sqrt{2} \sin ⁡\theta\) and \(\sqrt{6} \cos ⁡\theta\), respectively. If \(\pi \lt \theta \lt 2\pi\), find \(\theta\) for which \(f(\theta)=g(\theta)\).

The polar coordinates \((r,θ)\) corresponding to the cartesian coordinates \((1,-\sqrt{3})\) are,

Look at the graph of \(g(x)\).

If the function \(f(x)=\dfrac{x}{2}\) is drawn, for how many values of \(x\) is \(f(x)=g(x)\) (Assume the domain of g(x) is [0, 10])?

What is the value of \(\sin\left(\cos^{−1}\left(\frac{1}{2}\right)\right)+\sin\left(\cos^{−1}\left(\frac{\sqrt3}{2}\right)\right)\) ?

Which of the following options shows the range of \(2(1 − 2 \cos ⁡x)\)?

Which of the below graphs shows the polar function \(r = 1 + \cos ⁡θ \ ?\)

A polar function \(r = 1 − \sin{\theta}\) is plotted for \(\frac{3\pi}{2} \lt \theta \lt 2\pi\). Which of the below statements is true about the graph as \(\theta\) increases from \(\frac{3\pi}{2} \) to \( 2\pi?\)

Which of the following polar functions produces a limaçon with an inner loop?

For what values of \(\theta\) is \(\cos⁡ \theta \lt -\frac{1}{2} \ \) and \( \ \sin⁡ \theta \gt − \frac{1}{\sqrt{2}} \ \)?

(Note: \(\pi \lt \theta \lt 2\pi\))

The function \(h(x) = sin(2x + π/12)\) is defined on a restricted domain so that its inverse exists. Which of the following gives a valid restricted domain?

The temperature of a city during winters can be modeled using a function of the form \(f(t)=300−100 \sin \left(\frac{\pi \ t}{45}\right)\), where \(t\) is a specific winter day.

What is the trend in the city temperature on the 22^nd day \((t = 22)\)?

You may use a calculator.

A rose curve is defined by the equation \(r = \cos⁡(2θ)\). Which option shows the graph of the function in the interval \((0,2π)\)?

Which of the below expressions is equal to \(\dfrac{\sin ⁡x}{1 − \cos ⁡x} \ ?\)