If sin(x) = (1/4) and sec(y) = (7/4) , where x and y lie between 0 and π/2, evaluate sin(x + y).

Question

debbieg · Answer

Do you know the identity for sin(x+y)?

campbell_st · Answer

can you express sec in terms of cos... before you do anything...?

debbieg · Answer

It involves 4 parts: sinx, cosx, siny, cosy.

You are given sinx, so that's covered.

You are given secy, from which you can get cosy (do you understand how?)

From sinx and the fundamental identity, you can get cosx to within a +/- value.

From cosy and the fundamental identity, you can siny to within a +/- value.

You can plug these all back into the identity and evaluate the expression. The only thing I'm not clear on is what to do about the +/- on the 2 unknown values.... maybe someone can chime in if I'm missing something. I would have expected you to be told the quadrant for x and y in order to know the signs on cosx and siny....?

debbieg · Answer

Haha... I wasn't reading closely enough.... thought it said that x and y were between 0 and 2pi. I see now that it's 0 to pi/2, so disregard the issue of the signs on cosx, siny. Not an issue at all.