# Math Help - Two Trigonometry Problems

1. ## Two Trigonometry Problems

I have two problems

1) Express cot 138° 15' 10'' as the same function of a positive acute angle and then find its value.

2) Using exact values find the numerical value of tan 225
°+tan(-45°)

2. Originally Posted by Amy
I have two problems

1) [B]Express cot 138° 15' 10'' as the same function of a positive acute angle and then find its value.
We can write,

138°15'10''=180° - x
What is that x ?

Note, we can write,
180°=179°60'=179°59'60''
Thus, we can easily see from this that,
x=41°44'50''

Now use the identity,
cot (180°-x)=-cot x for x acute.

Thus,
cot (138°15'10'')=cot(180°-41°44'50'')=-cot(41°44'50'')

3. Originally Posted by Amy
2) Using exact values find the numerical value of tan 225[/B]°+tan(-45°)

Use the identity tan(180°+x)=tan x for accute x.

Thus,
tan 225°=tan(180°+45°)=tan 45°=1.

For the second tangent, tan(-45°), use the identity,
tan(-x)=-tan x.
Thus, tan(-45°)=-tan(45°)=-1.
Thus,
1+(-1)=0.