Find sin 2x, cos 2x, and tan 2x from the given information. sin x = -3/5, x in quadrant 3.

, ,

Step-by-step explanation:

The sine, cosine and tangent of a double angle are given by the following trigonometric identities:

According to the definition of sine function, the ratio is represented by:

Where:

- Opposite leg, dimensionless.

- Hypotenuse, dimensionless.

Since , measured in sexagesimal degrees, is in third quadrant, the following relation is known:

and .

Where is represented by the Pythagorean identity:

The magnitude of is found by means the Pythagorean expression:

Where is the adjacent leg, dimensionless.

If and , the value of is:

Then, the definitions for cosine and tangent of x are, respectively:

If , and , the values for each identity are, respectively:

and .

Now, the value for each double angle identity are obtained below:

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step-by-step explanation: