What is the point of trigonometric identities?

Trig identities are relationships between different trig functions. There are a lot of them. But they are rarely used.

Your other answers said that trig is used often in physics and engineering. That is true, but trig identities don't come up much at all. You should know where to find a list of them so you can look them up if needed. But I wouldn't memorize them.

I'm a math professor and I rarely ever use them.

Trigonometry is used widely throughout the world in subjects such as Physics , Electronics , Electrical, Mechanical, Civil and Chemical Engineering.

Trigonometric identities are ratios of the sides of triangle inside a circle with a radius of 1unit. The sine I

Of the able is the ratio of the opposite side over 1 and the cosine is the ratio of the adjacent side of the triangle over 1.

This is used in navigating, surveying, making maps and physics and engineering to solve real world problems. Al though not the same, which way do you screw the tap to turn the water to your house on after midnight when it is starting go rain, clockwise or counter clockwise? The answer is counter clockwise according to the right hand rule.

basically there are only 3 identities that you need to know

1) cos² Θ + sin² Θ = 1

2) cos ( Θ + µ ) = cos Θ cos µ - sin Θ sin µ

3) sin ( Θ + µ ) = sin Θ cos µ + cos Θ sin µ

this is assuming you know what is meant by sin w , cos w , tan w , sec w , csc w , cot w......

divide 1) by cos² Θ you get ( 4) 1 + tan² Θ = sec² Θ....

let Θ = µ in 2) yields (5) cos 2Θ = cos² Θ - sin² Θ = 1 - 2 sin² Θ ( using 1)) = 2 cos² Θ - 1 ( using 1)) and in 3) yields ( 6 ) sin 2Θ = 2 sin Θ cos Θ.

using ( 5 ) and solving for cos Θ you get cos Θ = ± √ ( [ cos 2Θ + 1 ] / 2 )..a half angle formula

Let's start with the most commonly used identity:

sin² x + cos² x = 1

This is simply the Pythagorean theorem used on the unit circle (which is why it's called the Pythagorean identity). This is very useful for converting sine to cosine and vice versa.

There are many other identities: reflections, shifts, sum and difference, multiple angle, sum to product (and vice versa). You can find a list of them here:

https://en.wikipedia.org/wiki/List_of_trigonometri...

These are tools that can be used to solve geometric problems. Mathematicians, scientists, and engineers all use them to solve equations. For example, if/when you learn calculus, you'll find that some expressions are easier to work with than others, and identities can help you get there.