Mathematical Scratchpad

Practice for test 3

Note. Some answers are provided.

  1. Explain why MATH graphically.

  2. If MATH

    1. Fnd the period of $f.$

    2. Find the asymptotes for $f.$

    3. Sketch $\tan \dfrac{x}{2}$and $\tan $ $x$ together.

    4. Sketch $\tan 2x$ and $\tan $ $x$ together.

  3. Find the function whose graph is the reflection of $y=\tan x$ ($y=\sin x;$ $y=\cos x$) along the $y-axis.$ [Ans. $y=\tan (-x),$ $y=\sin (-x),$ $y=\cos (-x).]$

  4. Find the function whose graph is the reflection of $y=\tan x$ ($y=\sin x;$ $y=\cos x$) along the $x-axis.$[Ans. $y=-\tan x,$ $y=-\sin x,$ $y=-\cos (x)$].

  5. For MATH Find

    1. $\sin \theta $ [answer: MATH

    2. $\cos \theta $ [answer: MATH

  6. For MATH Find

    1. $\sin \theta $ [ ans: MATH

    2. $\cos \theta .$ [ ans: MATH

  7. If MATH and MATH Find

    1. $\cos (\pi -t)$ [ans: $-\frac{4}{5}]$

    2. $\sin t.$ [ans: $\frac{3}{5}]$

  8. If $\sec \theta =4,$and MATHFind

    1. $\sin \theta .[$ans: MATH

    2. MATH [ans: $-\sqrt{15}]$

  9. Define a function $f$, whose graph is similar to the cosine function, $\cos x,$ and satisfies ALL the following conditions:

    1. the period of $f$ is $4\pi ,$

    2. the function $f$ has amplitude of $4,$

    3. the function $f$ has a maximum value of $2$ when $x=2\pi .$

Answer: MATH

This document created by Scientific WorkPlace 4.0.