If sin theta = 2/3 and sex theta < 0 , find cos theta and tan theta

Step-by-step explanation:

Trigonometric Formulas

To solve this problem, we must recall some basic relations and concepts.

The main trigonometric identity relates the sine to the cosine:

The tangent can be found by

The cosine and the secant are related by

They both have the same sign.

The sine is positive in the first and second quadrants, the cosine is positive in the first and fourth quadrants.

The sine is negative in the third and fourth quadrants, the cosine is negative in the second and third quadrants.

We are given

Find the cosine by solving

We have placed the negative sign because we know the secant ('sex') is negative and they both have the same sign.

Now compute the tangent

Rationalizing

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