# Thread: Find the exact values

1. ## Find the exact values

For each pair of values of sin(theta) and cos(theta), find the exact values of the four remaining trigonometric functions, when this is possible; otherwise find the four remianing functions to 3 significant figures:

sin(theta)= 3/5, cos(theta)= -4/5

sin(theta)= .9170001, cos(theta)= 3.98

2. Apply Pythagorean Theorem and find the missing value..

$x^2 + y^2 = r^2$

Where x being the adjacent side, y being the opposite side, and r is the hypotenuse.

Now that you got the values of x, y, and r, simply replace it in the 6 trigonometric ratios.

$\sin{\theta} = \frac{y}{r}$

$\cos{\theta} = \frac{x}{r}$

$\tan{\theta} = \frac{y}{x}$

$\csc{\theta} = \frac{r}{y}$

$\sec{\theta} = \frac{r}{x}$

$\cot{\theta} = \frac{x}{y}$

3. I got the first part but to be able to do the last part's of the question I would need more than one number. Should I put them over 1 or what? I am confused about what to do with sin(theta)= .9170001, cos(theta)= .398 since they are in decimal form.

4. Then convert them to fractions and reduce the fraction to it's lowest terms. You do know how to convert a decimal to a fraction, right?

5. Yes. I see now. Thanks!

6. Originally Posted by christenc05
For each pair of values of sin(theta) and cos(theta), find the exact values of the four remaining trigonometric functions, when this is possible; otherwise find the four remianing functions to 3 significant figures:

sin(theta)= 3/5, cos(theta)= -4/5

sin(theta)= .9170001, cos(theta)= 3.98
Let us do them in another way.

sin(theta)= 3/5, cos(theta)= -4/5

That means for angle theta,
opposite sde ...(opp)... = 3
hypotenuse.....(hyp)... = 5

So,
tan(theta) = opp/adj = 3/(-4) = -3/4
cot(theta) = adj/opp = (-4)/3 = -4/3
sec(theta) = hyp/adj = 5/(-4) = -5/4
csc(theta) = hyp/opp = 5/3

--------------------------------
sin(theta)= .9170001, cos(theta)= 3.98

That means for angle theta,
opposite sde ...(opp)... = 0.9170001
hypotenuse.....(hyp)... = 1