Question

Given that sin 64° = 9/10 and cos 64° = (√19)/10 find the following:
1. cot 64° =
2. cos -64° =
3. csc 64° =
4. csc -26° =
5. sec 244° =

Answer 1

since sin = y/r and cos = x/r, you have

x = √19
y = 9
r = 10

Now look at the other functions.

tan = y/x
sec = r/x
etc.

Answer 2

are these correct?
1. (√19)/9
2. √19/10
3. 1/10

and i'm not sure how to do 4 and 5

Answer 3

3. csc 64° = = r/y = 10/√19
4. csc -26° = -csc(26°) = -sec(64°) = -r/x = -10/√19
5. sec 244° = sec(180°+64°) = -sec(64°) = -r/x = -10/√19

For #4, recall that 64° and 26° are complementary angles. So, swap func and co-func. That's what the co- means

cosine(x) = sine(co-x)