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avatar+895 

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
avatar+8406 
+2

Note that   sin( 90° - a )  =  cos( a )      and      cos( 90° - a )  =  sin( a )      and      tan( 90° - a )  =  cot( a )

 

This might help you see why those are true....

 

 

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? smiley

 May 15, 2019
 #2
avatar+895 
+2

Yes, thanks for the help.

AdamTaurus  May 15, 2019

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