# If sin theta is equal to 2/3, theta not in quadrant 1, find tan theta?

By signing up, you agree to our Terms of Service and Privacy Policy

Here,

So, we have

Now , using trig.identity , we get

Hence,

By signing up, you agree to our Terms of Service and Privacy Policy

Given that ( \sin(\theta) = \frac{2}{3} ) and ( \theta ) is not in quadrant 1, we can use the relationship between sine and cosine in different quadrants to determine the sign of ( \cos(\theta) ). Since ( \sin(\theta) = \frac{2}{3} ) is positive, ( \cos(\theta) ) must also be positive because in quadrants where sine is positive, cosine is also positive.

Using the Pythagorean identity ( \sin^2(\theta) + \cos^2(\theta) = 1 ), we can solve for ( \cos(\theta) ) to find ( \cos(\theta) = \sqrt{1 - \sin^2(\theta)} ). Then, we can find ( \tan(\theta) ) using the relationship ( \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} ).

Substituting the given values, we have ( \tan(\theta) = \frac{\frac{2}{3}}{\sqrt{1 - \left(\frac{2}{3}\right)^2}} ). After simplification, we get ( \tan(\theta) = \frac{2}{\sqrt{5}} ). Therefore, ( \tan(\theta) = \frac{2\sqrt{5}}{5} ) because ( \sqrt{5} \times \sqrt{5} = 5 ).

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7