Year 11 Specialist (Unit 1 & 2) Trigonometric functions

Reciprocals of trigonometric functions

ACCOUNT REQUIRED

Unlock all 5 questions & worked solutions

You're viewing a free preview. Create an account to access the complete question set, step-by-step solutions, and progress tracking.

All Questions

Access the full question set for every topic.

Worked Solutions

Step-by-step explanations for every answer.

Track Progress

Mark questions right or wrong and monitor your growth.

It's Free

No credit card required - sign up in under a minute.

Questions

Question 1

75462

Sketch the graphs of \(y=\sin x\) and \(y= \dfrac{1}{\sin x}\) on the same set of axes, over the interval \(-2 \pi \le x \le 2 \pi\)

Answer

Refer to worked solutions

Worked Solution

\begin{align}
&y=\sin x: y=0 \\
&x=-2 \pi,-\pi, 0, \pi, 2 \pi \\
&y=\frac{1}{\sin x}: \text { asymptotes at: } \\
&x=-2 \pi,-\pi, 0, \pi, 2 \pi \\
&y=\sin x:\\
&y=1:\ x=-\frac{3 \pi}{2}, \frac{\pi}{2} \\
&y=-1:\ x=-\frac{\pi}{2}, \frac{3 \pi}{2}\\
&y=\frac{1}{\sin x}: \\
&\min \left(-\frac{3 \pi}{2}, 1\right)\left(\frac{\pi}{2}, 1\right) \\
&\max \left(-\frac{\pi}{2},-1\right),\left(\frac{3 \pi}{2},-1\right)
\end{align}

📚 Want More Questions?

There are 4 more questions available. Create your free account to access the complete question set with detailed solutions.

Get Full Access Already Have Account?