How do you find tan-theta when sin-theta equals -0.5736 and cos-theta is greater than 0?

Answer 1

-0.5736

Answer 2

First we must find what sign tan-theta will have.

Sin-theta is negative, which means that theta must be in the 3rd or 4th quadrant of a graph. (from π radians (180˚) to 2π radians(360˚))

Now because cos-theta is greater than 0, it is positive, and cos-theta is only positive for values of theta in the 4th or 1st quadrant. The only possible choice is the 4th quadrant.

Tan-theta equals sin-theta/cos-theta. Because sin is negative and cos is positive, tan-theta will be a negative value.

Now to find the numerical answer.

Sin-theta in a triangle is equal to the opposite/hypotenuse. In this problem,

-0.5736 is the opposite. And the hypotenuse for all values of theta would be 1.

Create a right triangle where the leg opposite to value theta has a value of 0.5736, and where the hypotenuse is 1.

With a right triangle set up you can now use the Pythagorean theorem

a2+b2=c2

Where a and b are values for the legs and c is the value for the hypotenuse.

Using b for the leg opposite value theta, you manipulate the equation to work with the values found and you get:

c2-b2=a2

Plug in the values for c and b now.

12-(-0.5736)2=a2

1-0.3290=a2

0.671=a2

square root both sides

√0.671=a

0.819=a

(all values are rounded off the the thousandths place)

Now that you have the values for leg a and b, you can find the value for tan-theta.

Tan-theta equals opposite/adjacent or b/a in this case.

-0.5736/0.819=tan-theta

-0.700≈tan-theta