If sin theta = -5/7 , which of the following are possible? a) cos theta = √24/7 , and tan theta = 5/√24 b) cos theta = -√24/7, and tan theta = 5/√24 c) sec theta = 7/√24 , and tan theta = -5/√24 d)sec theta = -7/5, and tan theta = 5/√24

Solution:

we are given that

As we know that

Substitute the value we get

Since

So here

As we know that

Hence the correct option is C.

It is given that

And according to pythagorean identity, we will get

Substituting the value of sin theta, we will get

and sec theta is the reciprocal of cos theta.

SO possible values of sec theta are

And tan theta is the ratio of sin theta and cos theta

So possible values of tan theta are

So the correct options are B and C .

You don't actually divide fractions. You multiply them. To multiply fractions use the "keep, change, flip method"
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original problem: 2/3 ÷ 1/3

You keep the first fraction, change the sign, and flip the second fraction:
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2/3 x 3/1 = 6/3 or 2