Question

An equation of the terminal side of an angle θ in standard position is given with a restriction on x. Sketch the least positive such angle θ, and find the values of the six trigonometric functions of θ. 3x+5y=0, x≥0

I have figured out how the line is needed to be sketched for 3x+5y, but am having a difficult time when trying to determine the 6 trigonometric functions.

Answer 1

tanθ=-3/5, the gradient of the graph.

The hypotenuse of a triangle with leg lengths 3 and 5 is √(9+25)=√34.

sinθ=-3/√34, cosθ=5/√34.

cotθ=-5/3, cosecθ=-√34/3, secθ=√34/5.

The sign of the trig value is determined by the quadrant containing the angle. θ is in quadrant 4, and the only positive trig values are cosine and secant. This angle measures 30.96º approx. below the x-axis (clockwise).

If measured in an anti-clockwise direction the angle is 360-30.96=329.04º.

The six trig values above are unaffected by what reference frame the angle is measured.