hi, $\displaystyle y=tan(\theta-45^\circ)$ in solutions it states it meets y-axis at -1 my question about this is how do i know that graph meets the y axis exactly at -1 ?
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at the $y$ axis $\theta = 0$ $\tan(0-45^\circ) = \tan(-45^\circ) = -1$
Your two axes are the $y$-axis and the $\theta$-axis. If you want to know when the graph meets one axis, set the variable for the other axis to zero. This gives $y = \tan (-45^\circ ) = -1$.