Use the given function values and trigonometric identities (including the relationship between a trigonometric function and its cofunction of a complementary angle) to find the indicated trigonometric functions.

Sorry for the mistake. They are two separate functions and i need to find a through d

sec Q = 5 tan = 2sqrt6

a) cos Q b) cotQ

c) cot(90 degrees - Q) d) sin Q

Mark, I see no change in the way you typed your question.

I objected to the line

sec Q = 5 tan = 2sqrt6

which makes no sense.
First of all 5tan is incomplete, there is no angle. I assumed it was 5tanQ
Secondly, the statement led to a contradiction, as I showed in the other post

I think what Mark means is that

Sec(theta)=5
Tan(theta)=2(sqrt of 6)
Which would make more sense :)

To find the indicated trigonometric functions, we can use the given function values and trigonometric identities.

a) To find cos Q, we can use the identity sec^2 Q = 1 + tan^2 Q. Since we are given sec Q = 5, we can substitute this value in the identity:

sec^2 Q = 1 + tan^2 Q
(5)^2 = 1 + (2√6)^2
25 = 1 + 24
25 = 25

Therefore, cos Q = 1.

b) To find cot Q, we can use the identity cot^2 Q = 1 + tan^2 Q. Since we are given tan Q = 2√6, we can substitute this value in the identity:

cot^2 Q = 1 + tan^2 Q
cot^2 Q = 1 + (2√6)^2
cot^2 Q = 1 + 24
cot^2 Q = 25

To find cot Q, we take the square root of both sides:

cot Q = ±5

Therefore, cot Q can be either 5 or -5.

c) To find cot(90 degrees - Q), we can use the identity cot(90 - x) = tan(x). Therefore, cot(90 degrees - Q) = tan(Q).

Given tan Q = 2√6, we know that cot(90 degrees - Q) = tan Q = 2√6.

d) To find sin Q, we can use the identity sec^2 Q = 1 + tan^2 Q. Rearranging the identity, we have tan^2 Q = sec^2 Q - 1. Substituting the given values:

tan^2 Q = (5)^2 - 1
tan^2 Q = 25 - 1
tan^2 Q = 24

To find sin Q, we can use the identity sin^2 Q + cos^2 Q = 1. Since we already know cos Q = 1 (from part a), we can substitute this value:

sin^2 Q + (1)^2 = 1
sin^2 Q + 1 = 1
sin^2 Q = 0

Taking the square root of both sides, we have:

sin Q = 0

Therefore, a) cos Q = 1, b) cot Q can be either 5 or -5, c) cot(90 degrees - Q) = 2√6, and d) sin Q = 0.