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## Trigonometry

### Course: Trigonometry>Unit 4

Lesson 5: Using trigonometric identities

# Using the tangent angle addition identity

Find the tangent of 13pi/12 without a calculator using the tangent angle addition identity. Created by Sal Khan.

## Want to join the conversation?

• whoa whoa whoa, where the heck did he get 15pi/12 - 2pi/12? is he just picking randomn fractions(angles or whatver)? By that reasoning, why can't I just use 3pi/12 plus 20pi/12?
• He picked them because 15pi/12-2pi/12=13pi/12, which is the angle we are trying to evaluate. Why did he pick those two angles to find the difference of (when there are many others that would also equal 13pi/12)? Because of what they simplify down to. The 15pi/12 simplifies to 5pi/4. We know how to find tan(5pi/4), which is 1. The same thing goes for 2pi/12. It simplifies to pi/6, and tan(pi/6)=1/sqrt(3).

Hope this helps!
• Isn't the slope change in y over change in x? Why does he use one point and just does y over x = slope?
• The line goes through the origin (0,0) and the point (x,y). So, the complete formula would be (y-0)/(x-0)=y/x.

So, if you are finding the slope of a line that goes through the origin, all you have to do is take y/x.

Hope this helps!
• why are the practice problems so much harder than what we learn in the video?
i feel like there are not enough videos here to go ahead to the parctice problem because he does not show how to solve so many of them
• You could read the article at the end of this section, this covers equations ranging from the inverse of sin to the reciprocal of tangent and the equations to solve the problems.
• In , Sal said we've proven tangent identities in another video. Where can I find that video?

I was trying to search the tangent identities but couldn't find a video with the sum and difference identities of the tangent.
• When Sal says the slope of the tangent on the unit circle is just the radius for 5pi/4 = 1, why is it different for pi/6?
• Since tangent is opposite divided by adjacent, the values in the 45-45-90 triangle are both the same so it'll just be 1.
• Why did Sal rationalize the variables last? I mean, I can see why that was a good idea since it was faster than just rationalizing them from the start, but is there a rule on when to rationalize or is it just common sense on when it's a good idea to rationalize now than later?

Edit: I notice he didn't have to rationalize this way.