the cosine model has the form 6 find the equation of the trigonometric functions graphed below 3 notes over 6 4 graph sine cosine and tangent functions equation of a sine function amplitude period complete cycle transformations of sin function transformations repped btw the function graphed below is known to be to the tangent and cotangent functions find the equation that best represents it f looking at the graph above we can see that there are certain times between 4 4 p m and 10 10 p m when the water will dip below 1 75 1 75 determining an equation from a graph when finding equations we can sometimes get confused about whether there is a reflection or a phaseshift unless we are given specific information to check take out your homework from last night ppt graphing sine and cosine transformations lesson transcript study com picture of graph of sine equality obtain equation from transformed sin graph deriving piecewise function equations from graphs modeling sine cosine warm up find both a sine and cosine equation for the the curve below is the graph of a sinusoidal function table x y sine function pa equation f x sin x obtaining piecewise functions from graphs 2 amplitude sine function piecewise continuous and noncontinuous 7 4 p eriodic g raphs and p hase s hifts identifying graphs sin transformations of csc and sec functions trig pa functions 4 notes over 6 4graphing a sine functions draw one cycle of the function s graph amplitude period below is a sketch of an unknown function find a likely candidate equation that could represent the function determining an equation from a graph example 2 find the equation of the sine curve in the graph below 5 restricted cosine function and it s inverse the function cos x is graphed below notice that this graph does not pass the horizontal line test example 1 determining the characteristics of a sine function based on its equation polynomial graph these two graphs make up the parabola shown above observe the graph below acos stands for arc cos which is the inverse of the cosine function inverse sin and cos graphs we see that the sine graphs are a rotation of the cosine graphs the cosine rose curves all have one petal aligned with the positive x axis 4 amplitude model the graph below shows the horizontal displacement of a pendulum from its rest position graphing sine and cosine functions a graphing calculator to graph the terplot of the data in the table below then find the sine function of best fit for the data 12 find a particular equation for the sinusoid function observing the graph we see that the model is vertically shifted by y 4 and oscillates about this line as noted above it has an amplitude of b 6