Evaluate Trigonometric Functions

Example on how to evaluate trigonometeric functions corresponding to question 6 in trigonometry_2.

Example 1


If $f(\theta)=tan(2\theta+\dfrac{\pi}{4})$ and $h(\theta)=\cos(\theta + \dfrac{\pi}{4})$, then $f(h(\dfrac{\pi}{4}))=$

  1. $-2$
  2. $-1$
  3. $0$
  4. $1$
  5. $2$

Solution


  1. First examine the 5 possible answer; we are asked to evaluate $f(h(\dfrac{\pi}{4}))$ given $f$ and $h$. In order to evaluate $f(h(\dfrac{\pi}{4}))$, we first evaluate $h(\dfrac{\pi}{4})$

    $h(\dfrac{\pi}{4}) =\cos(\dfrac{\pi}{4} + \dfrac{\pi}{4}) = \cos(\dfrac{\pi}{2})= 0 $

  2. We now substitute $h(\dfrac{\pi}{4})$ by $0$ in $f(h(\dfrac{\pi}{4}))$ and calculate $f(h(\dfrac{\pi}{4}))$ as follows

    $f(h(\dfrac{\pi}{4})) = f(0) = \tan (2(0)+\dfrac{\pi}{4})= \tan (\dfrac{\pi}{4})=1$

    Answer D