Trig Functions and Graphs (radians)

Hong Kong

Stage 4 - Stage 5

Consider the equation $3\sin\left(3x+\frac{\pi}{7}\right)=-\frac{11}{10}$3`s``i``n`(3`x`+π7)=−1110.

a

Which function would be graphed along with $y=-\frac{11}{10}$`y`=−1110 in order to solve the equation graphically?

b

Graph both of these functions using the graphing facility of your calculator. Hence state all solutions to the equation over the domain $\left[-\frac{13}{42}\pi,\frac{5}{14}\pi\right]$[−1342π,514π]. Give your answers correct to three decimal places separated by commas.

Easy

Approx a minute

Consider the equation $-5\cos\left(\frac{x}{2}+\frac{\pi}{5}\right)=-\frac{17}{10}$−5`c``o``s`(`x`2+π5)=−1710.

Consider the function $y=\sin\left(x-\frac{\pi}{3}\right)$`y`=`s``i``n`(`x`−π3).

Consider the function $y=\cos\left(x-\frac{\pi}{6}\right)$`y`=`c``o``s`(`x`−π6).

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