# Find the exact values

• Jul 9th 2008, 06:24 AM
christenc05
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
• Jul 9th 2008, 06:54 AM
Chop Suey
Apply Pythagorean Theorem and find the missing value..

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

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.

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

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

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

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

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

$\displaystyle \cot{\theta} = \frac{x}{y}$
• Jul 9th 2008, 07:20 AM
christenc05
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.
• Jul 9th 2008, 10:21 PM
Chop Suey
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? :)
• Jul 10th 2008, 05:21 AM
christenc05
Yes. I see now. Thanks!
• Jul 10th 2008, 01:48 PM
ticbol
Quote:

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