SOLUTION: If f(0) = sin0 and k(0) = tan0, find f(480)+k(390). Do not use a calculator and show fina answer please with steps. thanks

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Question 1152510: If f(0) = sin0 and k(0) = tan0, find f(480)+k(390). Do not use a calculator and show fina answer please with steps. thanks
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


The statement of the problem uses invalid notation; as a result, there is no way to find the answer.

Fortunately it is quite clear what the real meaning of the problem is.

If f(x) = sin(x) and k(x) = tan(x), find f(480)+k(390).

f(480) = f(480-360) = f(120) = sin(120)

k(390) = k(390-360) = k(30) = tan(30)

Use your unit circle to find the answers.
Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
.

They want you calculate sin(480°) + tan(390°).



The angle 480° is more than 1 full rotation, which, as you should know, is 360°.


So, the angle of 480° is equivalent to  480° - 360° = 120°,  and sin(480°) = sin(120°).


What is sin(120°), knows every student:  it is  .



The angle 390° is also more than 1 full rotation and is equivalent to 390° - 360° = 30°.  


Therefore,  tan(390°) = tan(30°).  What is  tan(30°),  knows any student:  it is  .



Therefore, the  ANSWER  to the problem's question is

   sin(480°) + tan(390°) =  + .



You may transform this expression further, if you want or if you need.

Solved, answered, explained and completed.

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Is my explanation clear to you in all details ?



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