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

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

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

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

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

AdamTaurus May 15, 2019

#1**+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?

hectictar May 15, 2019