Question 6, Exercise 9.1

Solutions of Question 6 of Exercise 9.1 of Unit 09: Trigonometric Functions. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan.

Find the period: $y=6 \sec(2 x-3)$

Solution.

Since period of the $\sec$ is $2\pi$, therefore $$\begin{align*} 6 \sec(2 x-3) & = 6 \sec(2 x-3+2\pi) \\ & = 6 \sec(2(x+\pi)-3) \end{align*}$$ Hence period of $6 \sec(2 x-3)$ is $\pi$.

Find the period: $y=\cos (5 x+4)$

Solution.

Since period of the $\cos$ is $2\pi$, therefore $$\begin{align*} \cos (5 x+4) & = 6 \cos(5x+4+2\pi) \\ & = \cos\left(5\left(x+\frac{2\pi}{5}\right)+4\right) \end{align*}$$ Hence period of $\cos (5 x+4)$ is $\dfrac{2\pi}{5}$.

Find the period: $y=\cot 4 x+\sin \frac{5 x}{2}$

Solution. (unable to solve)

Find the period: $y=7 \sin (3 x+3)$

Solution.

Since the period of $\sin$ is $2\pi$, therefore: $$\begin{align*} 7 \sin(3x + 3) &= 7 \sin(3x + 3 + 2\pi) \\ &= 7 \sin\left(3\left(x + \frac{2\pi}{3}\right) + 3\right). \end{align*}$$ Hence, the period of $7 \sin(3x + 3)$ is $\dfrac{2\pi}{3}$

Find the period: $y=5 \sin (2 x+3)$

Solution.

Since the period of $\sin$ is $2\pi$, therefore: $$\begin{align*} 5 \sin(2x + 3) &= 5 \sin(2x + 3 + 2\pi) \\ &= 5 \sin\left(2\left(x + \pi\right) + 3\right). \end{align*}$$ Hence, the period of $5 \sin(2x + 3)$ is $\pi.$

Find the period: $y=2 \tan 3 x+75 \cos x$

Solution.

(problem)

< Question 5(vi-x) Question 7 & 8 >