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# Find the Exact Value

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Find the exact value of each expression. Do not use a calculator.

$$sin(38^o)-cos(52^o)$$

$$tan(12^o)-cot(78^o)$$

$$\frac{cos(10^o)}{sin(80^o)}$$

$$\frac{cos(40^o)}{sin(50^o)}$$

May 15, 2019

#1
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Note that   sin( 90° - a )  =  cos( a )      and      cos( 90° - a )  =  sin( a )      and      tan( 90° - a )  =  cot( a ) sin( 90° - a )  =  cos( a )   is saying that line  r  is the same length as line  s .

cos( 90° - a )  =  sin( a )   is saying that line  b  is the same length as line  c .

tan( 90° - a )  =  cot( a )   is saying that   r / b  =  s / c

So.....

sin( 38° )  -  cos( 52° )

=   sin( 90° - 52° )  -  cos( 52° )

=   cos( 52° )  -  cos( 52° )

=   0

tan( 12° )  -  cot( 78° )

=   tan( 90° - 78° )  -  cot( 78° )

...Do you see where this one is going? Can you finish it?

$$\phantom{=}\qquad\frac{\cos(10°)}{\sin(80°)}\\~\\ =\qquad\frac{\cos(90° - 80°)}{\sin(80°)}\\~\\ =\qquad\frac{\sin(80°)}{\sin(80°)}\\~\\ =\qquad1$$

The last one is a really similar to previous one. Do you know how to do it now? May 15, 2019
#2
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Yes, thanks for the help.