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.

Question

sec Q = 5

tan Q = 2sqrt6

a) cos Q

b) cotQ

c) cot(90 degrees - Q)

d) sin Q

Answer 1

Ok, finally , now it makes sense
And now it is easy.

given: secQ = 5, then cosQ = 1/5

So we have a right angles triangle, where the hypotenuse is 5, the side adjacent to angle Q is 1, and the opposite to angle Q is 2√6

Notice that the second function, tanQ = 2√6 was not necessary, since we can see that from our triangle.

a) cosQ = 1/5
b) cotQ = 1/tanQ = 1/(2√6)
c) cot(90 - Q) = tan Q = 2√6
d) sinQ = 2√6/5

Answer 2

SIN(90-Q)/COSEC(90-Q)=COS(90-Q)/COSEC(90-Q)

Answer 3

SIN(90-Q)/COSEC(90-Q)+COS(90-Q)/COSEC(90-Q)=1