SOLUTION: I need to find the value of tan(theta) but the only value I have is sin(theta)=1/4 and it is in quadrant I. I know that (sin)(sin)theta + (cos)(cos)theta=1 so if sin(theta)= 1/

Algebra ->  Radicals -> SOLUTION: I need to find the value of tan(theta) but the only value I have is sin(theta)=1/4 and it is in quadrant I. I know that (sin)(sin)theta + (cos)(cos)theta=1 so if sin(theta)= 1/      Log On


   

Question 211542: I need to find the value of tan(theta) but the only value I have is sin(theta)=1/4 and it is in quadrant I.
I know that (sin)(sin)theta + (cos)(cos)theta=1 so if sin(theta)= 1/4 then sin(sin)theta =1/16... so cos(cos)theta=square root of 15/16.. and this is positive because the values are in quadrant I which is always positive. From there I know that sin(theta) over cos(theta) will give me tan(theta) but I dont know how to simplify from there. Can you help me with that?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

... Start with the first Pythagorean identity.


... Plug in


... Square 1%2F4 to get 1%2F16


... Subtract 1%2F16 from both sides.


... Multiply 1 by 16%2F16


... Combine the fractions.


... Subtract


... Take the square root of both sides. Note: because is in the first quadrant, this means that (ie cosine is positive). So we don't need to worry about the negative square root.


... Break up the square root.


... Take the square root of 16 to get 4.


-------------------------

... Move onto the tangent identity.


... Plug in and


... Multiply the first fraction by the reciprocal of the second fraction.


... Cancel out the common terms and simplify.


... Multiply the fraction by sqrt%2815%29%2Fsqrt%2815%29 (this will rationalize the denominator).


... Combine the fractions.


... Multiply


So if , then