Question

The straight line with equation y=3/4x makes an acute angle theta with the x-axis.

Find the value of sine 2 theta and cos 2 theta.

Answer 1

What you can do for this question is that you can do a rough plot of how the graph of this function would look like by choosing any 3 random values. This will give you a triangle that you can then use to find the trigonometric values.



So if you look at this figure, you know that tan (theta) is 12/9 or simplified, tan theta is 4/3

This means that theta = tan inverse of (4/3) = 53.13 degrees
2theta is 106.26 degrees

Now you can easily find the sine and cos of 2theta
sin 2 theta = sin 106.26 = 0.96
cos 2 theta = cos 106.26 =-0.28