Find the six trigonometric function????

Question

Find the value of the six trigonometric functions if the terminal side is on the line in the specified quadrant y=1/3 x in quadrant 3 one point on that line is (-6,-2)

 

I dont understand this question.

Answer 1

In trig, you have to know a couple things.

You have to know how to draw the triangle corresponding to the problem.

You have to know how to find sin, cos, and tan on that triangle.

Finding csc, sec, and cot are no problem after that.

 

This is hard to visualize without drawing it, so get out your paper.

 

Draw the x and y axis.

Plot the point (-6,-2) and draw a line from there to (0,0)

From your point, draw a line straight up to the x-axis.

That should give you a triangle. Got it?

 

If the triangle is drawn in this way, then...

 

sinθ = y / hypotenuse

cosθ = x / hypotenuse

tanθ = y/x

 

on your triangle, you should get y is -2, x is -6

 

Keep in mind negative numbers matter.

Don't forget how to find hypotenuse... x²+y² = hypot²

Also note that if you had chosen any other point on that line, your answer for sin,cos,tan should be the same.

 

After you find sin cos tan.

 

cscθ = 1/sinθ (you will get some fraction for sinθ, so just flip it over)

secθ = 1/cosθ

cotθ = 1/tanθ

 

Could you follow? What did you get for your answers?

 

sinθ = -2/root(40) = -1/root(10) = -root(10)/10

cscθ = -root(10)