Question

If tan theta= 15/8, then:

A. sec theta = 17/8
B. cos theta = 15/17
C. cot theta = 8/15
D. csc theta = 17/15

There's potentially more than one answer.

Answer 1

Well we know

\[\large tan = \frac{sin}{cos} = \frac{15}{8}\]

This tells us that sin = 15 and cos = 8

Answer 2

So a good hint, cos is not represented as a fraction..so B does not make sense

Answer 3

Now, Lets begin with A

\[\large sec \theta = \frac{1}{cos} = \frac{1}{8}\]

Secant can be written as 1/cos...and since we know cos = 8 we would have 1/8

So A is out as well

Answer 4

Now D

\[\large csc\theta = \frac{1}{sin} = \frac{1}{15}\]

cosecant can be written as 1/sin and since we know sin = 15...

So D is out

Answer 5

And finally C

\[\large \cot\theta = \frac{1}{tan} = \frac{1}{\frac{sin}{cos}} = \frac{cos}{sin} = \frac{8}{15}\]

Here we have our answer!

Answer 6

Is the key just memorizing when to use sin/cos/tan and SOACAHTOA or whatever?

Answer 7

it is incorrect to say sin theta is 15 and cos of theta is 8.
the outputs should be between -1 and 1

Answer 8

build a right triangle base on what is given then find the hyp

Answer 9

then you can find sin of theta cos of theta and so on based off that triangle

Answer 10

Refer to the one line calculation using Mathematica v9.