I don't understand how I'm supposed set the problem up or what theta is...
Use the given function value(s), and trigonometric identities (including the cofunction identities), to find the indicated trigonometric functions.
sec theta = 5, tan theta 2 * 6^1/2
a) cos theta
b) cot theta
c) cot (90 degrees - theta)
d) sin theta
To solve this problem, we first need to understand what the given trigonometric functions mean. Let's break it down:
1. sec theta = 5: The secant function (sec) is the reciprocal of the cosine function (cos). So, sec theta = 5 means that 1/cos theta = 5.
2. tan theta = 2 * sqrt(6): The tangent function (tan) is the ratio of the sine function (sin) to the cosine function (cos). So, tan theta = 2 * sqrt(6) implies sin theta / cos theta = 2 * sqrt(6).
Now, let's solve for the specific trigonometric functions:
a) cos theta:
We know that sec theta = 1/cos theta = 5. To find cos theta, we can take the reciprocal of 5, giving us cos theta = 1/5.
b) cot theta:
We can find cot theta by rearranging the equation tan theta = sin theta / cos theta = 2 * sqrt(6). Dividing sin theta and cos theta by cos theta, we get sin theta / cos theta = 1 / tan theta = 1 / (2 * sqrt(6)). Taking the reciprocal, we find cot theta = 2 * sqrt(6).
c) cot (90 degrees - theta):
Using the cofunction identities, cot (90 degrees - theta) = tan theta. We know that tan theta = 2 * sqrt(6).
d) sin theta:
To find sin theta, we can use the Pythagorean identity: sin^2 theta + cos^2 theta = 1. Since we know cos theta = 1/5, we can substitute it into the identity as follows: sin^2 theta + (1/5)^2 = 1. Solving for sin theta, we find sin theta = sqrt(24)/5.
So, to summarize:
a) cos theta = 1/5
b) cot theta = 2 * sqrt(6)
c) cot (90 degrees - theta) = 2 * sqrt(6)
d) sin theta = sqrt(24)/5
By understanding the given functions and applying relevant trigonometric identities, we were able to solve for the indicated trigonometric functions.
Theta is what we call the angle we are trying to find.
sec theta is the reciprocal of the cosine function. 1/cos theta = 5, so cos theta=1/5