Evaluate each expression

[jsh_aziza]

I need to evaluate each expression using exact values, and no calculators. For example sec 35 csc 55 - tan 35 cot 55. Now for values like 45, 30, and 60 degrees it's easy to figure out, but what about values in between like the equation above? Could you guys give me some tips. Thx.

 

[Deleted member 4993]

I need to evaluate each expression using exact values, and no calculators. For example sec 35 csc 55 - tan 35 cot 55. Now for values like 45, 30, and 60 degrees it's easy to figure out, but what about values in between like the equation above? Could you guys give me some tips. Thx.

convert it to sin and cosine first:

sec 35 csc 55 - tan 35 cot 55

= [1/cos 35] * [1/sin 55] - [sin 35/ cos 35] * [cos 55/sin 55]

simplify further and continue.....

remember

55 = 90 - 35

 

[nycfunction]

I need to evaluate each expression using exact values, and no calculators. For example sec 35 csc 55 - tan 35 cot 55. Now for values like 45, 30, and 60 degrees it's easy to figure out, but what about values in between like the equation above? Could you guys give me some tips. Thx.

You can draw a picture of the angles on the xy-plane as a first step. Since the period of the sine and cosine functions is 360 degrees, each full revolution can be ignored.

You were given 35 and 55. Question: How can we get 35 and 55 using one of the familiar trig values?

How can we get sec35? sec35 = 90 - 55

How can we get csc55? csc55 = 90 - 35

This is all we need to replace 35 and 55 for tan and cot, right?

We can use 90 for all 4 trig functions. Why? Again, since the period of the sine and cosine functions is 360 degrees, each full revolution can be ignored. We than have this:

(sec90)(csc90) - (tan90)(cot90) =

You should know that sec90 is undefined or does not exist. The same applies for tan90.

This leaves us with the trig expressions:

csc90 - cot90 =

csc90 = 1 and cot90 = 0

Then: 1 - 0 = 1

Final answer: (sec 35) (csc 55) - (tan 35) (cot 55) = 1

By the way, if you change every trig function given to sine and cosine as a first step, the answer would still be 1.[/color][/b]