Question

if sin of theta = 4/5 and theta is in quadrant 2. what is the value of tan theta

Answer 1

Remember that \[
\tan\theta=\frac{\sin\theta}{\cos\theta}
\]

Answer 2

Also remember that \[
\cos^2\theta+\sin^2\theta = 1
\]

Answer 3

Since it is the second quadrant, that means \(\cos\theta < 0\).

Answer 4

So we know \[
|\cos\theta | = \sqrt{1-\sin^2\theta}
\]based on the Pythagorean identity given earlier.

Answer 5

Think you can solve the rest of this?

Answer 6

is cos theta 3/5?

Answer 7

Remember that \(\cos\theta < 0\).

Answer 8

However, I will verify that \(|\cos\theta| = 3/5\).

Answer 9

is is 4/3

Answer 10

Another way to do this problem:

Answer 11

If \(\sin\theta\) is positive and \(\cos\theta\) is negative, then... should \(\tan\theta\) be positive or negative?