Example Question 10

Example corresponding to question 10 in trigonometry_2.

Example 1


What is $\sin x$ if $-7 \sin(-x) + 10 = 5$?
  1. $-5$
  2. $\dfrac{7}{5}$
  3. $-\dfrac{5}{7}$
  4. $\dfrac{5}{7}$
  5. $-\dfrac{1}{7}$

Solution


  1. We first solve the given equation for $\sin (-x)$.

    $-7 \sin(-x) + 10 = 5$

    $-7 \sin(-x) = 5-10$

    $-7 \sin(-x) = -5$

    $\sin(-x) = \dfrac{5}{7}$

  2. We now use the identity $\sin (-x) = -\sin x$ to obtain

    $\sin x = -\dfrac{5}{7}$

    Answer C