Trigonmetry Functions (radian circles)

[phat2107]

Homework Statement

If sin (x) = -6/7

what is cos(x) = ?
what is tan(x) = ?

the answers have to be in integer form, as in no decimals.
the "x" is supposed to be in quadrant 3

2. The attempt at a solution

This is in radians

so i did sin^-1 (-6/7) = -1.02969

the answer I am assuming is (x)

than cos (x) --> 0.5150 and since its in quadrant 3 this will -.5150
than tan(x) --> -1.664

im not sure if i am right soo far, but assuming i am. i tried using pythagoras to figure our what -0.5150 will be in decimal --> -(sqrt(13))/7

and tan --> and I am lost can't figure this out

any guide or assistance would be great thanks

 

[rock.freak667]

sin(x)=opp/hyp.

so if sin(x)=-6/7, what is opp and hyp?

When you get that, draw the angle x in the 3rd quadrant and construct the right angled triangle.

 

[Mark44]

Draw a right triangle inside a circle of radius 7. The sine function is positive in quadrants I and II and is negative in quadrants III and IV. Since you are given that sin(x) = -6/7, which quadrants can the angle x be in? For each of these, how long does the side adjacent have to be?

Your answers won't be in integers: they will be either rational numbers (the quotient of two integers) or the quotient of a radical and an integer.

 

[HallsofIvy]

You could also use the fact that $sin^2(x)+ cos^2(x)= 1$ to find cos(x) (remembering that the angle is in the third quadrant so cos(x) is negative.)

Then use the fact that tan(x)= sin(x)/cos(x).

In essence, both rock.freak667 and I are telling you, "yes, use the Pythagorean theorem".

 

[phat2107]

The teacher asked for fractions, so my mistake as putting it as an integer sorry..

I get how to get what tan(x) is but i don't understand how to find the fraction or what the fraction looks like

the cos one worked, ( i can check online if i got the right answer and i did) but tan is confusing me,

 

[rock.freak667]

The teacher asked for fractions, so my mistake as putting it as an integer sorry..

I get how to get what tan(x) is but i don't understand how to find the fraction or what the fraction looks like

the cos one worked, ( i can check online if i got the right answer and i did) but tan is confusing me,

tan(x)=sin(x)/cos(x)

or if you drew the triangle properly, you could find tan(x) by it's definition.

 

[Дьявол]

Use the fact that:

$$cos(x)=\sqrt{1-sin^2x}$$

If you know the value of sin(x) you can very easy find the value for cos(x) using the formula above ^^.

Then, when you know the values for sin(x) and cos(x), just substitute here tan(x)=sin(x)/cos(x) and find tan(x).

Regards.

 

[HallsofIvy]

Rock.freak667's point is that, since sine= opp/hyp, you can represent sin(x)= -6/7 as a right triangle with "opp"= -6 (on a graph, down 6 on the y-axis) and hypotenuse 7. You can use the Pythagorean theorem to determine that "adj" (measured on the x-axis) is $-\sqrt{7^2- 6^2}$ (negative square root because you are told that the angle is in the third quadrant and both x and y are negative there). Now that you know the lengths of all three sides of the right triangle, it is easy to find any of the trig functions. In particular, cos(x)= adj/hyp and tan(x)= opp/adj.