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### Two Trigonometry Questions

```
Date: 22 Jan 1995 17:52:53 -0500
From: Xin Li
Subject: Math Problem

1. SIN60 * COS60   2.      TAN45 * TAN3
```

```
Date: 22 Jan 1995 19:44:10 -0500
From: Dr. Sydney
Subject: Re: Math Problem

Dear Xin,

Hello!  We are glad you wrote to Dr. Math!  Let's see what we can do

1.  One way to approach your first problem is to take the values we know for
sin and cos of 60 and multiply them together.  I am assuming you mean 60
degrees, but if you mean radians the same ideas apply.

sin 60 = sqrt(3)
------
2

and cos 60 is 1/2, right?  So, sin 60 * cos 60 is sqrt(3)
-------
4

A different way to approach this problem is to use the property that:

sin 2x = 2sinxcosx.  So, sin 60 * cos 60 = sin 120
-------
2

But, really, this is making things more diffucult than they are!

So, see if you can do the same kind of thing on the second problem, and
write back if you have any more questions!

--Sydney, Dr. Math.
```

```
Date: 22 Jan 1995 20:35:21 -0500
From: Xin Li

For problem #1, we can use your first way of solving it, taking the known value
and multiply them together.  Knowing that SIN60(Degrees)=sqrt(3)/2 and COS60 =
1/2, we multiply sqrt(3)/2 by 1/2.  It comes out to be sqrt(3)/4.  Right? As for
problem two, let me think about it.
```

```
Date: 22 Jan 1995 20:43:30 -0500
From: Dr. Sydney

Dear Xin,

Yup!  That is right for problem #1.  Write back if you have any more
questions!

--Sydney
```
Associated Topics:
High School Trigonometry

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